What are my coincidences?

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11, 23, 47, 83, 131, 191, 263 - it is not a geometrical or arithmetical sequence, but it has interesting properties - sums of these numbers are additive prime numbers! These sums are: 2, 5, 11, 11, 5, 11, 11. Sum of digits in number 11 is 2.

11, 23, 47, 83, 131, 191, 263. It is probably the smallest such a sequence of additive prime numbers. Other as long sequences of additive primes appear to be hard to find or maybe even do not exist.

Numbers 2, 5, 11, 23, 47 are five first Thabit numbers.

Here are another sequences of prime numbers: http://mathforum.org/kb/message.jspa?messageID=415186.
A sequence 41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197, 223, 251, 281, 313, 347, 383, 421, 461, 503, 547, 593, 641, 691, 743, 797, 853, 911, 971, 1033, 1097, 1163, 1231, 1301, 1373, 1447, 1523, 1601 is mentioned here. There are 7 consecutive additive primes in that sequence (bolded), but not all seven have digit sum which is a prime number.
A sequence 17, 29, 53, 89, 137, 197, 269, 353, 449, 557, 677, 809, 953, 1109, 1277 also has seven consecutive additive prime numbers. However, not all these primes (bolded) are primes with additive primes as the sum of their digits.

From digits of the ascending arithmetical sequences:
- 11, 24, 37;
- 11, 42, 73;
- 13, 42, 71;
- 17, 24, 31;
phrase 21 7 can be formed.

Absolute values of common differences of sequences formed by reading these four sequences backwards are prime numbers.

It is interesting if someone else noticed pattern associated with prime numbers and digits: 1, 1, 2, 3, 4, 7. From these digits four ascending arithmetical sequences can be formed.
These sequences have middle terms and arithmetical means 42 or 24, sum of digits in these two numbers is 6 and arithmetical mean of digits is 3.
Sums of these three-membered arithmetical sequences are 72 and 126 and 72 and 126 are divisible by 18 (3+6+9).
Sum of digits in these sequences is 18 (3+6+9).

Products of digits in extreme terms of four arithmetical sequences mentioned above are 21:
- 1*1*3*7 = 21
- 1*1*7*3 = 21
- 1*3*7*1 = 21
- 1*7*3*1 = 21.

What is very interesting, two arithmetical sequences with three (21:7) numbers and sum 21 and arithmetical mean 7 (and middle term 7 also) can be formed from digits in extreme members of four ASes mentioned above:
- 1, 7, 13;
- 3, 7, 11.
In addition, these two ASes have the same products of their four digits as sums of three numbers which form them!
1*7*1*3 = 1+7+13 = 21
3*7*1*1 = 3+7+11 = 21
These arithmetical sequences (with the property mentioned above) are probably really rare. Another two which give such a property are 0, 0, 0 and 1, 2, 3.
0*0*0 = 0+0+0 = 0
1+2+3 = 1*2*3 = 6

The sequence 3, 7, 11 is especially interesting. It is formed by three additive prime numbers (3, 7, 11, sum of digits in 11 is 2 and it is a prime) and gives its descending counterpart (11, 7, 3) when read backwards. Another (even more interesting, because its CD is also an additive prime number - 2) sequence which has such a property is 3, 5, 7. Number 357 is the result of multiplication of 21 and 17. Numbers 21 and 17 can be formed from digits in the sequence 11, 24, 37.

First five Thabit numbers are additive prime numbers associated with digits 1, 1, 2, 3, 4, 7.
11, 23, 47 - third, fourth and fifth thabit numbers. First is 2, second is 5.
2, 5, 11 - three first Thabit numbers and sum of digits in 11, 23, 47!
Sum of 1st, 2nd and 3rd Thabit numbers is 18 and sum of digits in these three numbers is 18:2 = 9 (2 is the smallest Thabit number and sum of digits in the smallest term of 11, 23, 47 sequence).
Sum of 11, 23, 47 is 81, which is 18 read backwards. In addition, 81 is 9*9 and 18 is 2*9. Product of two of first factors in 2*9 and 9*9 is 2*9 = 18.
Sum of 18 and 81 is 99.

Thabit numbers are also called "321 numbers". Phrase "321" can be formed from digits in numbers 11, 24, 37.
All sums of digits in members of 11, 23, 47, 83, 131, 191, 263 are prime Thabit numbers 2, 5 or 11. Sums of digits in these sums are 2 or 5 - two first Thabit primes.

11, 24, 37. 11, 42, 73. 13, 42, 71. 17, 24, 31. Sum of these four sequences is 396. Number formed by digits: 3, 6, 9! It is divisible by 3+6+9 (18) - 369 is not divisible by 18 because it is an odd number and 18 is an even number.
396:18 = 22 (that two-digit number has the same sum of digits as product of them).
Arithmetical mean of sums of numbers in four sequences mentioned earlier is 99 (72+126+72+126):4 = (198+198):2 = 99.
Arithmetical mean of numbers in these four sequences is 396:12 = 33.
33 - arithmetical mean of digits in this number is 3.
33 - sum of digits in this number is 6.
33 - product of digits in this number is 9.

From combinations of digits of "miraculous sequences" 84, 42, 21 and 21, 42, 84 geometrical sequences with sums: 21, 42, 84, 63 can be formed.
1.
2+1 = 3
4+2 = 6
8+4 = 12
3, 6, 12 - geometrical sequence with sum 21!
2.
(2*1):(2:1) = 2:2 = 1
(4*2):(4:2) = 8:2 = 4
(8*4):(8:4) = 32:2 = 16
1, 4, 16 - geometrical sequence with sum 21!
3.
21:(2+1) = 21:3 = 7
42:(4+2) = 42:6 = 7
84:(8+4) = 84:12 = 7
7, 7, 7 - geometrical sequence with sum 21!
4.
2*1 = 2
4*2 = 8
8*4 = 32
2, 8, 32 - geometrical sequence with sum 42!
5.
(2+1)*(2:1) = 3*2 = 6
(4+2)*(4:2) = 6*2 = 12
(8+4)*(8:4) = 12*2 = 24
6, 12, 24 - geometrical sequence with sum 42!
6.
21 read backwards - 12
42 read backwards - 24
84 read backwards - 48
12, 24, 48 - geometrical sequence with sum 84!
7.
(2*1)*(2:1) = 2*2 = 4
(4*2)*(4:2) = 8*2 = 16
(8*4)*(8:4) = 32*2 = 64
4, 16, 64 - geometrical sequence with sum 84!
8.
21:(2-1) = 21:1 = 21
42:(4-2) = 42:2 = 21
84:(8-4) = 84:4 = 21
21, 21, 21 - geometrical sequence with sum 63 (21*3) and arithmetical mean 21!
9.
(2+1)*(2-1) = 3*1 = 3
(4+2)*(4-2) = 6*2 = 12
(8+4)*(8-4) = 12*4 = 48
3, 12, 48 - geometrical sequence with sum 63 (21*3) and arithmetical mean 21!

Difference between middle and the smallest term of sequence 21, 42, 84 is 21 (42-21). Sum of digits in number 21 is 3.
Difference between the largest and midlle term of that sequence is 42 (84-42). Sum of digits in number 42 is 6.
Difference between the largest and the smallest term of that sequence is 63 (84-21). Sum of digits in number 63 is 9. In addition, two digits forming that number are 3 and 6.

First three numbers of 11, 23, 47, 83, 131, 191, 263 sequence are numbers which can be formed by substracting 1 from the numbers forming geometrical sequence 12, 24, 48.

First three Thabit numbers (2, 5, 11) are numbers which can be formed by subtracting 1 from numbers which are sums of digits in numbers 21, 42, 84. These sum of digits are: 3, 6, 12.

Second, third and fourth Thabit numbers (5, 11, 23) are formed by subtracting 1 from numbers forming the geometrical sequence 6, 12, 24. Sum of these three Thabit numbers is 39.

First, third and fifth Thabit numbers (2, 11, 47) are formed by subtracting 1 from digits forming the sequence 3, 12, 48.

Some time ago I read about numbers 7, 11, 13 associated with certain text. It could be in summer or autumn 2017, relatively shortly after ending my third going to day hospital, which started 27.4.2017 and ended 24.7.2017. There is coincidence between numbers 7, 11, 13 and 27, 4 or 24, 7!

It is pretty large coincidence which I noticed maybe only today.
Sum of numbers 7, 11, 13 is the same as sum of numbers 27 and 4 or 24 and 7 and it is 31, a prime number.
Sum of digits in numbers 7, 11, 13 is the same as sum of digits in numbers 27 and 4 or 24 and 7 and it is 13, a prime number which is formed by reading digits in number 31 backwards!

In addition, sums of digits in numbers 7, 11 and 13 form the same digits as digits forming numbers 27 and 4 or 24 and 7!
7 = 7
1+1 = 2
1+3 = 4

Product of digits in numbers 7, 11, 13 is 21 (7*1*1*1*3). It is smaller than sum of these three numbers: 7+11+13 = 31. From the digits of numbers 7, 11, 13 two extreme members of arithmetical sequences: 11, 24, 37; 11, 42, 73; 13, 42, 71; 17, 24, 31 can be formed.

From digits of numbers 7, 11, 13 two ascending arithmetical sequences with sum of digits 21 and arithmetical mean 7 can be formed: 1, 7, 13 and 3, 7, 11.

I also found interesting triplet of additive prime numbers: 7, 29, 137. These are three additive prime numbers.
1. Sum of these three numbers is 173, an additive prime number which is formed by the same digits as the largest number in triplet 7, 29, 137.
2. Sums of digits in numbers 7, 29, 137 are all additive prime numbers:
7 = 7
2+9 = 11
1+3+7 = 11
3. Sum of sums of digits in 7, 29, 137 sequence is also an additive prime number!
7+11+11 = 29, sum of digits in 29 - 11, 11 occurs twice as a sum of digits in numbers 7, 29, 139; 29 is a member of "original" sequence.
4. Sum of digits in sums of digits in numbers of 7, 29, 137 sequence is also an additive prime number!
7+(1+1)+(1+1) = 7+2+2 = 11

So what does all of this prove?

This may be a proof of existence of supernatural reality.

I found two sequences of three consecutive additive prime numbers which have sums of numbers which is an additive prime number. They are:
- 5, 7, 11 (5+7+11 = 23; 2+3 = 5)
- 41, 43, 47 (41+43+47 = 131; 1+3+1 = 5).
Interestingly, smaller sequence is formed by sums of digits in numbers of larger sequence:
4+1 = 5
4+3 = 7
4+7 = 11
5711 is a prime number (although not additive) and 414347 is also a prime number (additive).

7, 11, 13 read backwards will form 31, 11, 7. Sum of numbers 7, 11, 31 is 49.
Interestingly, the sum of numbers 24 and 7 read backwards is also 49: 7+42 = 49.

Sequence: 7, 11, 13 can be associated with four dates from 2017 year:
- 27.4.2017 (start of my third going to day hospital)
- 24.7.2017 (end of my third going to day hospital, in the excerpt from it I got diagnoses of F84, F42, F21)
- 31.7.2017 (sum of digits is 21, three numbers forming that date are prime numbers, in the date digits 1, 3, 7 are present, as in the sequence 7, 11, 13, two arithmetical sequences with sum 21 and arithmetical mean 7 can be fromed from digits of that date (1, 7, 13; 3, 7, 11))
- 13.11.2017 (that day I had a visit with my psychiatrist and (at least probably) I was diagnosed with F84.5, F42.2, F21; all numbers in the date are primes, two arithmetical sequences with sum 21 and arithmetical mean 7 can be fromed from digits of that date (1, 7, 13; 3, 7, 11); from digits in that date the sequence 7, 11, 13 can be formed; numbers formed by two last digits in numbers in the date 13.11.2017 are prime numbers).

Yesterday I wrote about 7, 11, 13 and it was 13.11.2018, yesterday I did not notice that coincidence.

Today I noticed that certain film on YouTube has 169 likes and 31 dislikes. 169 = 13*13. Sum of digits in number of views of that film had sum of digits 21.

Phrases: 21.7 or 147 can be formed from digits in numbers of 11, 42, 73 sequence.

Product of digits of numbers used in that sequence is 168 (84+84), 168 would be fourth member of geometrical sequence starting with 21, 42, 84.
1*1*4*2*7*3 = 1*8*21 = 168
Sum of numbers of that sequence is 126 (11+42+73).
Difference between product of digits in 11, 42, 73 and sum of numbers in 11, 42, 73 is 168 - 126 = 42.

Sum of numbers in sequence 11, 24, 37 is 72.
Product of digits forming numbers 11, 24, 37 is the same as product of digits forming numbers 11, 42, 73 and it is 168.
Difference between product of digits in numbers 11, 24, 37 and sum of numbers in that arithmetical sequence is 168-72 = 96. Number 96 is formed by digits 9 and 6 and difference between 9 and 6 is 3.

Today I typed phrase 21 42 84 in Google and first result was about my topic started in one of Polish forums. I am interested if someone else noticed peculiar properties of 21, 42, 84 sequence and wrote about them in the Internet. Maybe I am the only human in history who noticed them?

How does it prove, or even suggest "the existence of a supernatural entity"?

My coincidences are in my opinion quite impresive and convincing. They are so numerous. It could be hard to say why they may prove existence of supernatural entities. I do not believe in "pure coincidence". I do not need coincidences to believe in One Supreme Being, I would rather suppose that my coincidences are "products" of unclean spirits. Large frequency of my coincidences may be a proof of their supernatural origin. There may be too much coincidences in my life to think that they are just result of "common mathematical chance".

25.11.2018 I typed in Google transliteration of Russian term for a creature from certain computer game, about which I watched film 14.10.2018. In the description of third link in the results there were three words for item which I called V in earlier posts! About month ago I typed the same or similar phrase in Google and there was Polish term for V in third link in results! In Polish language first, second, fifth, sixth, seventh letters of the name of V form a part of Polish name of certain creature from the game about which film I watched 14.10.2018, these creatures were present in the film which I watched that day.

There is also something interesting in the sequence formed by raeding the sequence 33, 42, 51 backwards - resulting sequence is also an arithmetical sequence with common difference 9 and it is 15, 24, 33.

06.12.2018 - some coincidences happened. That day I saw the date written as 6.12.18. Numbers: 6, 12, 18 form an arithmetical sequence (AS) which is interesting! Members of that AS are results of multiplicating numbers 3, 6, 9 by two. Sums of digits in numbers forming that sequence are 6, 3 (1+2) and 9 (1+8), sum of digits in the sequence is 18. 18 is also sum of 3, 6, 9. There are 3 numbers in the sequence: 6, 12, 18.

In addition, at the late evening of 6.12.2018 I noticed that the arithmetical sequence 11, 15, 19 has the same product of its six digits as sum of its three numbers! That sequence is notoriously coincident with another sequence with 15 as the middle term and arithmetical mean - 12, 15, 18:
1. Both ASes (11, 15, 19 and 12, 15, 18) have three numbers in them.
2. They have six digits in any of them.
3. Sum of digits in these two ASes is 18 (3+6+9).
4. Their arithmetical mean and middle term are the same (15), sum of three numbers forming them is 45 in both cases.
5. First digits of members forming these three sequences have the same sums (1+1+1 = 3) and are the same digits.
6. Sums of second digits have the same sums (15).
7. First and second digits in both ASes form another ASes (1, 1, 1 and 1, 5, 9 or 1, 1, 1 and 2, 5, 8 ).

I had big coincidence 18.12.2015. Last time I had coincidence with two dates associated with 18 - 06.12.2018 and 15.12.2018. Sums of digits in numbers formed by two last digits in numbers forming these dates sorted ascendingly form the "Tesla's arithmetical sequence" - 3, 6, 9.

I noticed that 1*1*1*5*1*9 = 11+15+19 at 06.12.2018, nine days before 15.12.2018. Numbers formed by two last digits in numbers in date 15.12.2018 form an arithmetical sequence with sum 18 when sorted ascendingly. Sums of digits in these numbers are 3, 6, 9 and one of members is a sum of digits in sequence 12, 15, 18.

6, 12, 18 and 11, 15, 19 and 12, 15, 18 (associated with both 18.12.2015 and 15.12.2018) are three-membered arithmetical sequences with sums of digits equating 18 (3+6+9)!

Interestingly, the day which will be nine days after 15.12.2018, also has 18 as the sum of digits of two last digits in its date - 24.12.2018. Numbers: 24, 12, 18 sorted ascendingly form an arithmetic sequence - 12, 18, 24. Sums of digits in numbers of that sequence are 3, 9 and 6, if they are sorted ascendingly, they form "Tesla's arithmetic sequence" - 3, 6, 9.
The difference between 06.12.2018 and 24.12.2018 is 18 (3+6+9) days. Two last digits in these dates form number 18.

Today I noticed two arithmetical sequences associated with codes of mental disorders in ICD-10 with which I was diagnosed in day hospital when I was going to it in IV-VI 2016. I was diagnosed with:
- F21 (schizophrenia-type (schizotypal) disorder)
- F42.2 (mixed obsessive-compulsive disorder)
- F65.8 (other sexual preference disorder, I do not wat to write about evil details of it)
- F84.5 (Asperger's syndrome, a pervasive developmental disorder).

First digits in codes of these four mental disorders (digits just after F) form an arithmetical sequence which has four terms! It is 2, 4, 6, 8. From that sequence two three-membered sequences can be formed: 2, 4, 6 (sum 12) and 4, 6, 8 (sum 18, arithmetical mean 6, just like in the case of 3, 6, 9).

Numbers after dots in codes F42.2, F65.8 and F84.5 sorted ascendingly form an arithmetical sequence 2, 5, 8.
I think that there may be relatively large chance for being diagnosed with three conditions which numbers after dots will form arithmetical sequence (for example someone might be diagnosed with F32.1 (moderate depressive episode), F42.2 (mixed OCD) and F60.3 (emotionally labile personality (Polish: osobowość chwiejna emocjonalnie), for example borderline personality disorder).

I think that there may be larger chance for being diagnosed with four diagnoses which have numbers forming four-membered arithmetic (or eventually geometric) sequence after letter in the code than the chance for being diagnosed with three diagnoses in which cases numbers after the letter in the code form geometric or arithmetic sequence.

Sequences: 11, 15, 19 and 12, 15, 18 have interesting property - sum of products of digits in their numbers is 15, which is arithmetic mean of these sequences and middle term of them.

(1*1)+(1*5)+(1*9) = 1+5+9 = 15
(1*2)+(1*5)+(1*8) = 2+5+8 = 15

There are also three another sequences which produce such a phenomenon:
- 13, 15, 17;
- 14, 15, 16;
- 15, 15, 15.

The sequence 11, 15, 19 is somewhat coincident with 3, 7, 11 - 15 and 19 are two next members of (infinite) arithmetic sequence starting with 3, 7, 11. 11 is the member which is shared by two arithmetical sequences which have the same product of digits of numbers forming them as the sum of numbers forming these sequences.

I had coincidence with another five-membered sequence with 11 as third (medium) member earlier. This sequence was not arithmetic nor geometric and was formed by five first Thabit numbers (which are in addition additive prime numbers). That sequence is: 2, 5, 11, 23, 47. First three Thabit numbers are sums of digits in third, fourth and fifth Thabit numbers.

I might say that there are two sequences which have five members and have 11 as the middle member which are important in my life:
- 2, 5, 11, 23, 47;
- 3, 7, 11, 15, 19.

In Google I found only one result for "2, 5, 11, 23, 47" "3, 7, 11, 15, 19" (both sequences were in quotation marks, both sequences were in one question for search engine).

12, 15, 18 forms an arithmetic sequence when written backwards: 81, 51, 21. Sum of that AS is 153.
11, 15, 19 forms an arithmetic sequence when written backwards: 91, 51, 11. Sum of that AS is 153.
Sums of "original" sequences are 45.
153-45 = 108.
108 = 6*(3+6+9) - sum of 3, 6, 9 multiplicated by arithmetical mean of 3, 6, 9.

Wow, am I ever out of the loop. I thought synchronicity is meaningful coincidence (Jung). But I have no recognition of what you're doing with all those numbers.