What are my coincidences?

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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).

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!

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.

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.

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).

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.

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.

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).

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.

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.

Why someone placed encounter with huge egg which stuck in the hole in certain computer game? Was it reference to something, like Big Hole (anus of alien lifeform from "Evolution" movie)? I may think that satan or demons inspired producers of the game to place Giant Egg encounter in it in the purpose of giving me large coincidences. Why quite many coincidences are associated with the book which is considered holy by Muslims, not Christians? In my mind the idea that God made some of my coincidences or permitted them in purpose may be present.

Coincidence with two or three quranic triplets (7, 29, 139; 7, 11, 14; 7, 2, 4) is huge. It is associated with quite many themes of my coincidences:
- 21 7 (moderately),
- 3, 6, 9 (relatively mildly),
- "miraculous quartet" of arithmetic sequences (very much),
- 24.7 and 27.4; 13 and 31 (very much),
- "giant egg" (5, 23, 421, very much).

Probability of coincidence between 7, 29, 139 and 5, 23, 421 is rather really low. 139 and 421 - numers have not to be sorted ascendingly or descendingly to form geometric sequences, there are only two such numbers whihc have 3 digits - 139 and 421, exactly.

I noticed two sets of numbers which I named "miraculous quintets". They are: 3, 7, 11, 15, 19 and 2, 5, 11, 23, 47. What links them?
- both have 5 numbers,
- two smallest numbers in both of them are one-digit,
- two smallest numbers in both of them are (additive) prime numbers,
- three largest numbers in both of them have two digits,
- third (middle) member in both of them is 11.

3, 7, 11, 15, 19 - arithmetic sequence with sum of numbers 55 and arithmetic mean 11 which has common difference 4.

2, 5, 11, 23, 47 - first five Thabit numbers. All of them are additive primes!

Very interesting are triplets formed by three smallest and three largest numbers in these quintets.

For 3, 7, 11, 15, 19 they are 3, 7, 11 and 11, 15, 19. Both are arithmetic sequences which have the same sums of numbers as products of digits forming them! Very interesting!
3*7*1*1 = 3+7+11 = 21
1*1*1*5*1*9 = 11+15+19 = 45

For 2, 5, 11, 23, 47 they are 2, 5, 11 and 11, 23, 47. Smaller triplet is formed by sums of digits of numbers in the larger one (1+1 = 2, 2+3 = 5, 4+7 = 11)!
Both triplets formed by consecutive Thabit primes are coincident with 3, 6, 9!
For first, 2, 5, 11:
1. Number of numbers is 3.
2. Arithmetic mean of numbers is 6.
3. Sum of digits is 9.
4. Sum of numbers is 18.
5. Arithmetic mean of sums of digits in numbers is 3 (((2+5+(1+1))/3 = (2+5+2)/3 = 9/3 = 3).
6. Difference between the middle and the smallest number in the triplet is 3 (5-2).
7. Difference between the largest and the middle term in 2, 5, 11 is 6 (11-5).
8. Difference between the largest and the smallest term in that triplet is 9 (11-2).
9. Three differences mentioned above form "Tesla's arithmetic sequence" - 3, 6, 9!

For second, 11, 23, 47:
1. Number of numbers is 3.
2. Number of digits is 6.
3. Sum of numbers is 81 which is 9x9; 81 has sum of digits 9.
4. Sum of digits is 18 which is 9+9 and 81 read backwards; 18 has sum of digits 9.
5. Arithmetic mean is 27 which is 3x9 and 3x3x3.
6. Difference between the middle and the smallest number in the triplet is 12 (23-11).
7. Difference between the largest and the middle term in 11, 23, 47 is 24 (47-23).
8. Difference between the largest and the smallest term in that triplet is 36 (47-11).
9. Three differences mentioned above form arithmetic sequence with sum 72; sums of digits in these differences are... 3, 6, 9!

21, 42, 84. Most coincident geometric sequence. By swapping digits in its numbers we receive 12, 24, 48. Sums of digits in both sequences are 3, 6, 12. All three sequences are coincident with 3, 6, 9:

- 42-21 = 21; 84-42 = 42; 84-21 = 63 -> 21, 42, 63 -> 2+1 = 3; 4+2 = 6; 6+3 = 9 -> 3, 6, 9
- 24-12 = 12; 48-24 = 24; 48-12 = 36 -> 12, 24, 36 -> 1+2 = 3; 2+4 = 6; 3+6 = 9 -> 3, 6, 9
- 6-3 = 3; 12-6 = 6; 12-3 = 9 -> 3, 6, 9

The same numbers are associated with 11, 23, 47 and numbers formed by swapping digits in numbers 11, 23, 47 - 11, 32, 74. Sums of digits in these sets of numbers are: 2, 5, 11.

- 32-11 = 21; 74-32 = 42; 74-11 = 63; 21, 42, 63 -> 2+1 = 3; 4+2 = 6; 6+3 = 9 -> 3, 6, 9
- 23-11 = 12; 47-23 = 24; 47-11 = 36; 12, 24, 36 -> 1+2 = 3; 2+4 = 6; 3+6 = 9 -> 3, 6, 9
- 5-2 = 3; 11- 5 = 6; 11-2 = 9 -> 3, 6, 9

My mentality: it's clear proof that Tesla's saying about the magnificience of 3, 6, 9 points at you (or, more precisely, your coincidences and ideas)!

I noticed something associated with arithmetic sequence 33, 42, 51. It was noticed 28.05.2020. I made first digits in numbers forming that sequence bases of powers while second digits were exponents of powers. I received:
3^3 = 3x3x3 = 27
4^2 = 4x4 = 16
5^1 = 5 = 5
Numbers: 27, 16, 5 form arithmetic sequence. Ascending counterpart of 27, 16, 5 is 5, 16, 27. It has arithmetic mean 16, sum of numbers 48 and common difference 11. Bith bases of powers and their exponents form arithmetic sequences which have common differences which have absolute vaule 1 (3, 4, 5 and 3, 2, 1).
Sums of digits in 27, 16, 5 are: 9, 7, 5. These numbers form arithmetic sequence with sum of numbers 21 and arithmetic mean 7. 21 and 7 form most coincident double for me. Absolute value of common difference of 9, 7, 5 is 2.

Numbers: 33, 42, 51 are associated with arsenic, molybdenum and antimony - three elements which names were for me neologisms when I was about 13 - 16 years old in meaning - vulgar words for buttocks, penis and external female genitals. It started because of the name of element with atomic number 33 ("arsenic", in Polish "arsen" - it is obvious to notice that four first letters in these two words form rude word for buttocks in British English). I suppose that I have that coincidence thanks to British "a-word". Without it I would probably not form such silly neologism which gave me coincidences many years later. Maybe names for molybdenum ("molibden") and antimony ("antymon") were considered nice in certain way for me so I decided to "promote" them? Now I do not consider words "arsen", "molibden" and "antymon" (and their counterparts in other languages) as vulgarisms.