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What are my coincidences?
Supernatural phenomena 13%  13%  [ 3 ]
Delusions, symptoms of psychosis 33%  33%  [ 8 ]
Ideas of reference 4%  4%  [ 1 ]
Effects of mere mathematical chance 50%  50%  [ 12 ]
Total votes : 24

nca14
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10 Feb 2019, 5:56 pm

At the beginning of that month I had large coincidence associated with buying paroxetine-containing medication.

1. It was 1.2.2019.
2. I paid 11,73 PLN.
3. I bought 3 packages of drug, 30 tablets in each, one tablet contains 20 mg of paroxetine.

The coincidence is associated mainly with numbers:
- 21.7,
- 3, 6, 9
- 21, 42, 84.

From digits of price of three packages two ascending arithmetic sequences with sums of numbers 21 and arithmetic means 7 can be formed:
- 1, 7, 13
- 3, 7, 11.
These sequences are formed by non-composite numbers.

Product of digits in number 11,73 is 21 (1*1*7*3 = 21).
Product of digits in number 11 is 21 times smaller than product of digits in number 73.
Arithmetic mean of numbers 11 and 73 is 42.
Sum of numbers 11 and 73 is 84.

One package of medication has 30 tablets.
30 tablets contain about 600 mg of paroxetine.
3 packages contain 90 tablets.
90 tablets contain about 1800 mg of paroxetine.
Digits which are not zeros form numbers: 3, 6, 9, 18 (18 is the sum of 3, 6, 9).
In these results of multiplication there were one or two zeros. Two times one zero, two times two zeros. There is a zero in the date 1.2.2019 and two numbers 2 and two numbers 1.

We have three numbers associated with the medication: 30, 20 and 3. Let's multplicate two of them:
30*20 = 600
20*3 = 60
30*3 = 90
In all three multiplications at least one number 3 was present.
Digits in products which are other than zeros are all from 3, 6, 9 group (namely 9 and two 6s). There are three digits: 9, 6, 6. Their sum is... 21 and arithmetic mean is... 7!

From digits in the date 1.2.2019 three-membered arithmetic sequence with two-digit numbers can be formed:
- 19, 20, 21.
Number 19 is quite important for me. One of my first large coincidences was associated with events from 19.9.2014, from that date two numbers 19 can be formed. 19 has also "private" meanings for me.
Number 20 is associated with amount of paroxetine in one tablet in medication which was bought. It is also the arithmetic mean of the sequence: 19, 20, 21.
Number 21 is "notoriously" coincident for me. Two numbers 21 can be formed from digits of the date: 1.2.2019.



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07 Mar 2019, 5:31 pm

One of my first coincidences was associated with three biggest Abrahamic religions: Christianity, Islam, Judaism. It happened 19.9.2014. I photographed Jewish cementery with matzevahs with Hebrew letters and a part of Catholic cementery with crosses. It was that day of the week during which Crucifixion of Christ happened and which is considered the rest day by many Muslims. It was 19th day of the month which is dedicated to Holy Cross in Catholic religion. Two numbers 19 can be formed from the digits of the date 19.9.2014. I read before starting of the coincidences that 19 is "special" number for some Muslims. About 11 p.m. I used the smartphone which was used to make the photographs of cementeries to watch posts written by another individual who was diagnosed with Asperger's syndrome. On some of posts which I saw 19.9.2014 Catholic or Jewish cementeries were present (with crosses or matzevahs with Hebrew letters, respectively). I saw one post from 19.7.2013 (in summer time), which was the youngest of posts in which that person with ASD wrote about cementeries.

Today I noticed that in date 19.7.2013 are the same digits like in the date 7.3.2019 (today). They are: 0, 1, 2, 3, 7, 9.
Five largest numbers (except zero) are highly coincident for me. From digits: 1, 2, 3, 7, 9 four-membered arithmetic sequence (AS) can be formed! It is: 1, 3, 9, 27. Quotient - 3.
Four largest numbers (except zero and one) are also coincident. From digits: 2, 3, 7, 9 three-membered AS can be formed: 3, 9, 27. Its sum is 39 and arithmetic mean is 13. Sum of digits in that sequence is 21 and arithmetic mean of sums of digits in these three numbers is 7!

I had coincidences with numbers associated with certain book. I read about some of them in second half of 2017. It looks dangerous for my religion! But I had coincidences with it. It looks from the biblical perspective that Quran was written by demons, I do not want to promote heresies, but I had quite many coincidences with something considered miracles (especially numerical, mathematical) of the book which is considered holy by Muslims. I read a lot about Quran's miracles (and knew about some of them before IX 2014) last time, I admit that they can look impressive, but belief in infallibility of Bible do not allow to consider Quran as final book from The Almighty. It is interesting why I have many coincidences with numerical miracles of Quran. I may have ideas that I have to spread knowledge about its mathematical miracles to the entire world and that I will destroy Christianity due to numerical miracles of Quran. I do not want to deprave anyone! It looks very bad and dangerous. Something like combination of reference, grandiose and messengership delusions.

So first coincidence with Quran mathematical miracles was associated with the triplets:
- 7, 29, 139 (numbers of: verses, words and letters in first surah),
- 7, 11, 13 (sums of digits in numbers forming triplet 7, 29, 139)
- 7, 2, 4 (sums of digits in sums of digits in numbers 7, 29, 139).

First triplet:
- three numbers,
- six digits,
- only one digit occurs two times and that digit is 9,
- from first digits of the numbers in 7, 29, 139 phrase "21 7" can be formed,
- sum of digits other than 2, 1 and 7 (9, 3, 9) is 21 and arithmetical mean of these three digits is 7 (again coincidence with 21 7),
- product of six digits forming that triplet is divisible by 7 and 21 or 3, 6, 9; it is 3402 (21*3*6*9).



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08 Mar 2019, 11:42 am

Five "sorts" of digits are found in triplet 7, 29, 139: 1, 2, 3, 7, 9. Number 12379 is a prime.

I found four arithmetic sequences with prime numbers as extreme members and common differences which are formed by the same digits (in the sequences are present such digits: 1, 1, 2, 3, 4, 7):
11, 24, 37 (CD 13),
11, 42, 73 (CD 31),
13, 42, 71 (CD 29),
17, 24, 31 (CD 7).

1. Sums of numbers in these sequences are 72 or 126, the same as in three-membered arithmetic sequences with middle terms 24 or 42 formed from digits: 1, 2, 3, 3, 4, 5.
2. Arithmetic means in four sequences above are 24 or 42, just like in three-membered arithmetic sequences with middle terms 24 or 42 formed from digits: 1, 2, 3, 3, 4, 5.
3. Sums of extreme members in four sequences above are 48 or 84, just like in three-membered arithmetic sequences with middle terms 24 or 42 formed from digits: 1, 2, 3, 3, 4, 5.
4. Sums of digits in numbers forming four sequences mentioned above form ASes with sum of numbers 18 and arithmetic means of these numbers 6 - the same is in the case of "Tesla's arithmetic sequence" (3, 6, 9) and the sequence 33, 42, 51.
5. Sums of numbers in these four sequences divided by arithmetic means of sums of digits in numbers forming four sequences above are 12 or 21, like in the case of sequences: 15, 24, 33; 33, 42, 51; 13, 24, 35; 31, 42, 53 and 12, 24, 48; 21, 42, 84.
6. Sums of numbers in these four sequences divided by sums of digits in numbers forming four sequences above are 4 or 7, like in the case of sequences: 15, 24, 33; 33, 42, 51; 13, 24, 35; 31, 42, 53 and 12, 24, 48; 21, 42, 84.
7. There are 3 numbers in all of four ASes and these four sequences have 6 digits in any of them.

So these four sequences are in some way coincident to 21.7; 3, 6, 9 and 21, 42, 84. Large coincidence. 21.7 and 3, 6, 9 may look as the keys for many coincidences.

In four sequences above five "sorts" of digits appears. They are: 1, 2, 3, 4, 7. 12347 is an additive prime number.



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15 Apr 2019, 4:44 pm

15.4.2019 I have large coincidence associated with four five-digit three-membered ascending arithmetic sequences (ASes) formed by five of digits from that date. Almost year ago, in the same day of week, 16.4.2018, I had another large coincidences associated with something which I wrote in the notebook.

These four sequences are:
- 5, 12, 19 (common difference 7),
- 9, 12, 15 (CD 3),
- 1, 15, 29 (CD 14),
- 9, 15, 21 (CD 6).
Two first sentences were quite well known to me before 15.4.2019, I noticed that two with arithmetic means (AMs) 15 also can be formed by digits 1, 1, 2, 5, 9 at 15.4.2019, maybe at least in the case of 1, 15, 29 it was my first noticing it in my life.

Product of CDs of ASes with AMs 12 is 21 (7*3). 7 is the smallest number in the phrase "21 7" and 3 is the smallest number of AS 3, 6, 9.
Product of CDs of ASes with AMs 15 is 84 (14*6). 14 is arithmetic mean of numbers 21 and 7 and 6 is AM of numbers 3, 6, 9.

Extreme terms of the sequence 9, 15, 21 are the largest numbers in the phrases: 21 7 (21) and 3, 6, 9 (9).

Product of 21 and 84 is 1764, which is 42*42. 42^2 is also the product of products of arithmetic means and smallest numbers in phrases: 21 7 (AM 14, smallest number in the phrase 7, product of these two - 98) and 3 6 9 (AM 6, smallest number in the phrase - 3, product of these two - 18).

I had next large coincidence with three very coincident phrases:
- 21 7
- 3, 6, 9
- 21, 42, 84.



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23 Apr 2019, 4:54 pm

I had another coincidence with alleged numerical miracles in islamic scripture last times. I found such a page: https://pl.scribd.com/document/36754980 ... -Primalogy. On it such a text can be found:

Quote:
Quran Primalogy
New Discovery – Nov, 2nd 2017
Primalogy structure in the number of words vs chapters

Fact #1 : There is 23 (prime and also additive prime) chapters with number of words as primes.
Fact#2 : The first 11 (prime and also additive prime) chapters total words number is 797 (prime and also additive prime).
Fact#3: The last 11 (prime and also additive prime) chapters total words number is 10037 (prime and .also additive prime).
Fact#4 : If we combine 797 and 337 (center chapter number of words) and 10037,we obtain 79733710037 which is prime and also additive prime.
Fact#5 : The total number of words of all the chapters is 11171 (prime and also additive prime).

036:053 Soon We shall show them Our signs in the horizons and in their own souls until it becomes clear to them that He is the Real. Is it not sufficient that your Lord is witness to all things?

So the Quran looks like a masterpiece of the fallen angels for a Christian...

This text is very coincident with:
- 2, 5, 11, 23, 47 (first five Thabit numbers which are additive primes, they are known for me since XI 2018);
- 27.4.2017;
- 24.7.2017;
- 11, 23, 47, 83, 131, 191, 263 (sequence of 7 additive prime numbers with additive primes being three first Thabit numbers as the sums of digits).

Almost all bolded numbers (23, 11, 797, 10037, 79733710037, 11171) in the text mentioned above are additive primes with additive primes being Thabit numbers as their sums of digits!
There is only one exception - 337, which has non-additive prime 13 as the sum of digits.
3, 7, 13 are three numbers associated with number 337 (its digits and sum of digits), sum of these three numbers is 23 - Thabit prime with another Thabit prime as sum of digits.
In addition, 13 is the sum of 1st and 3rd Thabit number - 2+11.
Two dates from 2017 are coincident with numbers 2, 11 and 23. 27.4.2017 and 24.7.2017 have sums of digits 23 and have sums of numbers being 2048. 2048 is 11th power of 2 (2^11)! What is more, the date in the text is Nov 2nd, 2017 - 2.11.2017! Numbers 2 and 11 again! In addition, two (2) numbers 11 can be formed from digits of last bolded number in the text above (from digits of 11171)! Amazing!



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28 Apr 2019, 4:34 pm

I noticed that in the decade 2011 - 2020 there were 21 dates with all six digits: 0, 1, 2, 3, 7, 9 in them. These six digits are present at least once in prime numbers bolded on the slide about chapters of Quran with prime numbers as sums of words in them.

These dates are:
* in 2013 (6 dates):
1. 09.07.2013
2. 19.07.2013
3. 29.07.2013
4. 07.09.2013
5. 17.09.2013
6. 27.09.2013
* in 2017 (7 dates):
1. 09.03.2017
2. 19.03.2017
3. 29.03.2017
4. 03.09.2017
5. 13.09.2017
6. 23.09.2017
7. 30.09.2017
* in 2019 (8 dates):
1. 07.03.2019
2. 17.03.2019
3. 27.03.2019
4. 03.07.2019
5. 13.07.2019
6. 23.07.2019
7. 30.07.2019
8. 31.07.2019

Numbers of dates in years form arithmetic sequence: 6, 7, 8, which has sum 21 and arithmetic mean 7.



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01 May 2019, 1:17 pm

On one page mentioned earlier there were seven numbers which were bolded (bolded by me below have not Thabit number as the sum of digits, underlined have not Thabit numbers as the number of digits in them):
- 23
- 11
- 797
- 10037
- 337
- 79733710037
- 11171
Most of numbers above are not only additive primes, but also have Thabit numbers as the sum of digits (6 of 7) and Thabit number as number of digits (5 of 7).

Let's look at the only number which has not 321 number (another term for Thabit number) as the sum of digits - 337:
1. There is one digit which occurs only once in that number - 7.
2. There is one digit which appears more than one time - it is 3.
3. Product of 3 and 7 (single digits occurring in number 337) is 21 and sum is 10 (which is the same sum as in the case of 21 7).
4. Number of digits in number 337 is 3.
5. Sum of digits which repeat themselves is 6 (3+3).
6. Product of digits which repeat themselves is 9 (3*3).
7. Product of all three digits in 337 is divisible by 7 and 21 and it is 63.
8. In number 63 occurs only digits 6 and 3, sum of digits in 63 is 9.
9. Product of digits in number 63 is 18, which is the sum of numbers 3, 6, 9.
So number 337 is quite coincident with 21 7 and 3, 6, 9! Three digits, many coincidences.

Two numbers which have not 321 number as number of digits (797 and 337) are also coincident with 21 7 and 3, 6, 9...
1. Both numbers have the same number of digits - 3.
2. Two three-digit numbers have together 6 digits.
3. Sum of these six digits is 36 (6*6, 6^2) and arithmetic mean of these digits is 6 - the same as arithmetic mean of the sequence 3, 6, 9.
4. Only one number appears only once in all six digits forming these two numbers together - that number is 9.
5. Arithmetic mean of sums of digits in these two numbers is 18 (3+6+9), it is ((23+13):2).
6. Only one of digits appears in both numbers 797 and 337 - that digit is 7.
7. Sum of digits which appears in both numbers together (two 7s from 797 and one 7 from 337) is 21, in addition, by concatenating numbers two (2) and one (1) we will receive 21; furthermore, sum of 7s in 797 is 14 and sum of 7s in 337 is 7, by concatenating 14 and 7 we will receive 147 (21*7).
8. Products of 7, 9, 7 and of 3, 3, 7 have the same sum of digits (9 - they are 441 and 63, respectively) and are divisible by 21; in addition, larger of these products is 7 times larger than smaller.
9. One third of all six digits in numbers 797 and 337 together is 3 (two 3s from six digits).
10. Sum of numbers 797 and 337 is 1134, which is a divisor of products of digits: 2, 1, 7, 3, 6, 9 (2268 - it is 1134*2) and a divisor of product of numbers: 21, 7, 3, 6, 9 (23814 - it is 1134*21).



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13 May 2019, 4:28 pm

14.10.2018 I saw (first) "specific" encounter in certain computer game. In it there was body of a man which has four-letter word at the end of his "name" in that game. In 2019 I saw second, another "specific" encounter from the same game and there were remains of body of another man, who had another four-letter word in the end of the name of himself. Both words not only have the same number of letters, but also have the same first and third letters! And the number of four-letter words with these first and third letters is relatively small! I had large coincidences due to these encounters.

Today I found that the author of the songs which I heard some time ago has four-letter name with the same first and third letters. I saw that word after that in certain TV programme, about 9:30 p.m. It was a surname. The person had name which had the same two first letters as second word in the name of second encounter mentioned earlier. Shortly after coincident surname, a coincident name was visible in TV - it has the same first, second and fourth letters as the name in first encounter in itself the name and was a four-letter word. It was not the end of coincidences with four-letter words on the same letter today evening... Today I thought about certain other four-letter word with the same first and third letters as words in the name of men from two "specific" encounters and I saw that word on certain forum about 10 p.m. Even that was not the end of coincidence. I typed certain three-word Polish phrase about 10 p.m. and under first link I saw Polish verb (in third person, present time) which was four-lettered, had the same first three letters as the word at the end of the name of man in second encounter! I also typed phrase associated with another "sort" of the game in which two encounters mentioned earlier were present and in third link I noticed... the word which was present in the name of man from first encounter!



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14 May 2019, 1:07 pm

Some days ago I saw a screenshot from Russian computer game on which something giant was visible. There was also "descrpition" or something alike in one of corners of the screenshot. That giant think had the name which have three letters and the same last letter as first word (a three-letter one) in the name of first specific encounter mentioned in previous post. The name of giant thing (a noun) was present in two places at the screenshot. What is more, the word present in the name of Big W (noun symbolised by W) encounter appears to appear three times on the screenshot!

I noticed numbers 5, 23, 421 somewhere. 5 and 23 were in "first" part, 421 - in other. 5 and 23 are Thabit numbers and digits from three-digit number form a geometric sequence with sum of digits 7, are the same as second digits in numbers of sequence: 84, 42, 21. From digits of 421 numbers 21 and 42 can be formed, 4 and 21 also can be formed at the same time (product of 4 and 21 is 84).

All three numbers are additive prime numbers with additive prime numbers as their sums of digits! What is more, the sum of these three numbers is an additive prime number also (449). Sum of digits in 5, 23, 421 is a prime number (although not additive one) and is the same as sum of digits in the sum of these three numbers (4+4+9 = 17 = 5+2+3+4+2+1). There are six digits in the phrase: 5, 23, 421, they are: 1, 2, 3, 4, 5, while 2 appears two times. 33, 42, 51 - also six digits, also: 1, 2, 3, 4, 5 (although 3 here appears two times, not 2).

Triplet: 5, 23, 421 is ever more coincident with prime numbers than 7, 29, 139. Sum of 5, 23, 449 is a prime number, even an additive one (449 - sum 17, a prime), while sum of numbers: 7, 29, 139 is a composite number divisible by 5 and 7 (175). Sums of digits in 5, 23, 421 are 5, 5, 7 - three additive prime numbers (one repeats oneself - 5, it is a Thabit numbers) while not all sums of digits in the case of 7, 29, 139 not all sums of digits are additive prime numbers (7, 11, 13) - 13 has sum of digits 4 and 4 is not a prime number (it is divisible not only by 1 and 4, but also by 2), from divisors of 4 number 421 can be formed.



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14 May 2019, 7:40 pm

Number formed by concatenation of 5, 23, 421 is not a prime number (although other combination of 5, 23, 421 - 542123 formed by 5, 421, 23 is a prime). 729139 formed by 7, 29, 139 is a prime, but 713929 is not.
71113 (formed by 7, 11, 13) is not a prime, 557 formed by concatenating of sums of digits in 5, 23, 421 is a prime.
5, 5, 7 - these numbers form prime factorization of the sum of numbers 7, 29, 139, which is 175.
I experienced coincidences with two triplets of additive prime numbers - 5, 23, 421 and 7, 29, 139.

I read about 5, 23, 421 on certain page associated with the game very similar to that with Big W specific encounter.
I probably saw also screenshots of two other specific encounters from Russian game with Big W. In one of them there could be found numbers 14 and 6 - 14 is arithmetic mean of 21 and 7 and 6 is arithmetic mean of 3, 6, 9; in addition, the product of 14 and 6 is 84. On second screenshot from another encounter there was a person with the name present in the name of certain other specific encounter (in which there was an item with black cat) in that game.

Today I saw the word which has four letters and has the same first, third and fourth letters as last word in the name of the man whose remains were present in the special encounter in which item with black cat could be found.



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23 May 2019, 12:16 pm

I found triplet 7, 29, 139 before I found triplet 5, 23, 421.

There are two coincident triplets: 7, 29, 139 and 5, 23, 421.
Sum of first numbers (and digits in them) in them is:
7+5 = 12.
Sum of digits in second numbers forming these triplets:
2+9+2+3 = 11+5 = 16.
Sum of digits in third numbers forming these triplets:
1+3+9+4+2+1 = 13+7 = 20.
Three sums mentioned above form arithmetic sequence - 12, 16, 20. Its sum - 48, arithmetic mean - 16, sum of digits - 12.

Sum of digits in triplet 7, 29, 139 is 31 and sum of digits in triplet 5, 23, 421 is 17. Difference between 31 and 17 is 14 and is the same as difference between 21 and 7.
Sum of digits which repeat oneself in triplet 7, 29, 139 is 18, because only 9 is repeating there. 9+9 = 18.
Sum of digits which repeats oneself in triplet 5, 23, 421 is 4, because only 2 is repeating there. 2+2 = 4.
Difference between 18 and 4 is also 14 (the same as difference between 21 and 7).

Sum of digits in 139 is 13 and sum of digits in 421 is 7. Numbers 13 and 7 are common differences of two of four arithmetic sequences from "miraculous quartet" (11, 24, 37; 17, 24, 31). 13 and 7 concatenated form 137. It is an additive prime number which was the nickname of certain user on certain Polish forum with whom I chatted certain night in 2019. Product of digits in 137 is 21, one of digits is 7.

From digits of 31 and 17 two interesting arithmetic sequences can be formed: 1, 7, 13 and 3, 7, 11. They have sum of digits 12, sum of numbers 21 and arithmetic mean of numbers 7. Products of digits forming these sequences are the same as their sums (21).



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26 May 2019, 12:34 pm

There is another interesting thing in triplets 7, 29, 139 and 5, 23, 421 (combined).
Sum of first numbers in these two triplets is 12 (7+5).
Sum of second numbers in these two triplets is 52 (29+23).
Sum of third numbers in these two triplets is 560 (139+421).
We have three numbers: 12, 52, 560.

There is something very coincident in them.
Sum of digits in first sum is 3.
Sum of digits in second sum is 7.
Sum of digits in third sum is 11.
Numbers: 3, 7, 11 form an arithmetic sequence with sum of numbers 21, arithmetic mean of numbers 7, sum of digits 12 and common difference 4.
Numbers: 3, 7, 11 are additive prime numbers.
Product of digits in 3, 7, 11 is 21 and is the same as the sum of numbers forming that sequence.
From digits of 3, 7, 11 another arithmetic sequence with sum 21 and arithmetic mean 7 can be formed: 1, 7, 13. It is formed by non-composite numbers, like 3, 7, 11.

12, 52, 560 - there are 7 digits and their sum is 21.
Something interesting happen when we consider numbers in F21, F42.2, F84.5. If we leave number in code without a dot as it stands and multplicate numbers before dots by numbers after them, we receive:
- 21 (from F21)
- 84 (42*2, from F42.2)
- 420 (84*5, from F84.5).
What we received? A triplet very similar to 12, 52, 560, because:
1. Both 12, 52, 560 and 21, 84, 420 are composed from two two-digit numbers and one three-digit number.
2. Both triplets have number with 0 as last digits in the largest number in them.
3. Both triplets have sums of digits 21 and are composed by 7 digits.

Sum of 12, 52, 560 is 624 and sum of 21, 84, 420 is 525. Both numbers have sum of digits 12 and arithmetic mean of digits 4. 12 and 4 is quite similar to 21 and 7 and coincident with it, because:
1. Both 12.4 and 21.7 have the same quotient - 3 (12:4 = 3, 21:7 = 3).
2. Both are composed by two-digit number and one-digit number, digits forming two-digit number are the same in both phrases.
3. Both have products of digits which are their arithmetic means and differences between larger and smaller numbers:
- 1*2*4 = 8 = 12-4 = (12+4):2,
- 2*1*7 = 14 = 21-7 = (21+7):2.
4. Sums of digits in two-digit number multiplicated by one-digit number give two-digit number:
- (1+2)*4 = 3*4 = 12,
- (2+1)*7 = 3*7 = 21.
5. Absolute values of products of differences of numbers in larger numbers (12 and 21) and smaller numbers (4 and 7) are smaller numbers (4 and 7):
- (1-2)*4 = (-1)*4 = -4, |-4| = 4,
- (2-1)*7 = 1*7 = 7.



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05 Jul 2019, 4:36 pm

Most coincident arithmetic or geometric sequences for me are 21, 42, 84; 3, 6, 9; 6, 13, 20 and 33, 42, 51. Most coincident double is 21 7, 13 and 31 is also pretty coincident. Last time I noticed that 12 4 is also quite coincident.

Sums of digits of first, second and third members of triplets 5, 23, 421 and 7, 29, 139 form arithmetic sequence which has many coincidences with 12 and 4.

- 5+7 = 12,
- 2+3+2+9 = 16,
- 4+2+1+1+3+9 = 20.

Received arithmetic sequence presents properties described in points below:

1. Sum of digits of 12, 16, 20 is 12.
2. Arithmetic mean of sums of digits of numbers in that sequence is 4 (in addition, these sums are additive primes: 3, 7, 2).
3. Number of terms in that sequence is 3, 3 is 12:4.
4. Smallest member of 12, 16, 20 is 12.
5. Middle term of that sequence is 16, 16 is 12+4.
6. Arithmetic mean of 12, 16, 20 is 16, 16 is 12+4.
7. Difference between the largest and the smallest member of that sequence is 8, 8 is 1x2x4 and 12-4.
8. Sum of numbers of 12, 16, 20 is 48, 48 is 12x4.
9. Common difference of that sequence is 4.
10. Quotient of sum of numbers in 12, 16, 20 and number of digits in these numbers together (6) is 8 (48:6), 8 is 1x2x4 and 12-4.



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12 Jul 2019, 4:51 pm

I found six triads of triplets associated with numbers 3, 6, 9; 12, 24, 36 (which have sums of digits 3, 6, 9) and 21, 42, 63 (which also have sums of digits 3, 6, 9).

Difference between the middle and the smallest numbers of these triplets is 3 or 12 or 21 (has sum of digits 3). Difference between the largest and the middle numbers of these triplets is 6 or 24 or 42 (has sum of digits 6). Difference between the largest and the smallest numbers of these triplets is 9 or 36 or 63 (has sum of digits 9).

* 0, 3, 9 - 0, 12, 36 - 0, 21, 63 (all three can be formed from digits of 30.9.2016, two larger are formed from digits of sequence 6, 13, 20)
* 1, 4, 10 - 10, 22, 46 - 1, 22, 64 (two larger can be formed from digits of date 24.6.2016, which is very coincident with 21, 42, 84)
* 2, 5, 11 - 11, 23, 47 - 11, 32, 74 (very coincident for me)
* 3, 6, 12 - 12, 24, 48 - 21, 42, 84 (very coincident and all three are geometric sequences)
* 4, 7, 13 - 22, 34, 58 - 22, 43, 85
* 5, 8, 14 - 23, 35, 59 - 32, 53, 95 (the smallest can be associated with the date 14.8.2015 - 5th year in the decade 2011 - 2020, 8th month of year, 14th day in month, I was taken by ambulance to the psychiatrist that day)

For 6, 9, 15 there are no two larger triplets as for smallest triplets above. I found 6 triads of triplets, in one triad there is 9 numbers (not always different ones).



nca14
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13 Jul 2019, 4:55 pm

Numbers forming first, second and third triplets formed by differences between larger and smaller members of triads of triplets mentioned in previous post form arithmetic sequences:
- 3, 6, 9
- 12, 24, 36
- 21, 42, 63
First numbers: 3, 12, 21 form arithmetic sequence in which all numbers have 3 as sums of digits. Common difference - 9.
Second numbers: 6, 24, 42 form arithmetic sequence in which all numbers have 6 as sums of digits. Common difference - 18.
Third numbers: 9, 36, 63 form arithmetic sequence in which all numbers have 9 as sums of digits. Common difference - 27.

3, 6, 9 --> 1(3+6+9)
12, 24, 36 --> 4(3+6+9)
21, 42, 63 --> 7(3+6+9)

Numbers bolded form number 147 (which is product of 21 and 7) when concatenated.



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15 Jul 2019, 4:43 pm

Some days ago I noticed that all three ascending three-digit three-membered arithmetic sequences with sum 18 and arithmetic mean 6 can be formed from sums of digits in numbers of arithmetic sequences formed by six digits present in the sequence 33, 42, 51. Constant sequence with these sum and arithmetic mean also can be formed from sums of digits in sequence(s) formed by these six numbers. These sequences are very similar to (or even the same as) "Tesla's arithmetic sequence" - 3, 6, 9.

33, 42, 51 - sums of digits: 6, 6, 6 (constant geometric and arithmetic sequence)
15, 24, 33 - sums of digits: 6, 6, 6 (constant geometric and arithmetic sequence)
31, 42, 53 - sums of digits: 4, 6, 8 (ascending arithmetic sequence)
13, 24, 35 - sums of digits: 4, 6, 8 (ascending arithmetic sequence)
12, 33, 54 - sums of digits: 3, 6, 9 (ascending arithmetic sequence)
21, 33, 45 - sums of digits: 3, 6, 9 (ascending arithmetic sequence)
14, 33, 52 - sums of digits: 5, 6, 7 (ascending arithmetic sequence)
25, 33, 41 - sums of digits: 7, 6, 5 (descending arithmetic sequence)

Amazing! Sequences above have six digits and five "sorts" of digits which form five-membered arithmetic sequence (1, 2, 3, 4, 5).
"Giant egg" (5, 23, 421) also has 6 digits and 5 different digits is used in it - they are the same as in sequences above. Last digits in numbers of "giant egg" form arithmetic sequence 5, 3, 1, which has the sum 9 and in which sum of digits other than 3, 6, 9 is 6 (5+1), the sequence has 3 digits and has arithmetic mean 3.