NLD, NVLD

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.

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.

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 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)!

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.

Some time ago I noticed three books, one above another. On the "highest" of them there was number 10, on "middle" - number 7, on the "lowest" - number 4. These three numbers form an arithmetic sequence with sum 21 and arithmetical mean 7! Amazing! 21.7 coincidence again! In addition, from digits of the sequence 4, 7, 10 another AS with sum of numbers 21 and arithmetic mean 7 can be formed! It is 0, 7, 14 (ascending). What a coincidence :!:

I started my third regular going to day hospital 27.4.2017 and ended it 24.7.2017. The same digits, the same sums of numbers. From digits in one of these two dates three ASes can be formed:
- 4, 7, 10 (common difference 3),
- 2, 7, 12 (CD 5),
- 0, 7, 14 (CD 7).
Common differences of these three ASes sorted ascendingly form unique arithmetic sequence - 3, 5, 7. It is formed by prime numbers only and has a prime number as the common difference (that number is 2). It is ONLY such an arithmetical sequence! Sequences: 1, 3, 5, 7 and 1, 3, 5 are not formed by prime numbers only, because 1 is not a prime number (although it is also not a composite number).

In second half of 2017 I read about certain three numbers. First digits in these numbers will form 21 7 when placed in appropiate way. Sum of three remaining digits is... 21 and arithmetic mean of these three digits is 7. Product of six digits forming that triad of numbers is divisible by 21, 7, 3, 6 and 9. One digit occurs two times in these numbers and that digit is nine. Four other digits in that triad occur only once.

I wrote quite much about my coincidences. Many of them would be not present if I would receive diagnoses of schizophrenia instead of schizotypal disorder. Without 21.7 many coincidences with 3, 6, 9 would be smaller, maybe even unnoticed.
21 is 7th member of infinite arithmetic sequence starting with 3, 6, 9.
20 (number in the ICD-10 code of schizophrenia) is not a member of that sequence.

In X 2014 a lecturer who has the same surname as my sister quite frequently talked about McDonald's. McDonald's was associated in my mind with MCDD (multiple-complex developmental disorder). I use the abbreviation MCDD on Polish Asperger's syndrome forum at 10.10.2008. In 2011-2012 there was a woman on that forum who suspected that she has MCDD. She wrote that she was diagnosed with, for example, Asperger's syndrome, schizotypal disorder, obsessive-compulsive disorder, schizophrenia. I also had these diagnoses in my life, three first of them at the same time. In 2014 I used quite often the abbreviation McDD on that forum and had coincidences with McDD. 14.10.2014 I noticed advertisement of McDonald's in bus with which I rode to the studies. I noticed also green clover leaf in that bus on another advertisement and 14.10.2014 an individual with aucorigia wrote the post about clover which might be associated with signs from supernatural forces, in topic in which that post was written first post after mine was written by another individual with aucorigia who had grey cat and clover on own user's image!

Both dates: 16.4.2018 and 18.4.2016 have 4, 6, 8 as last digits in numbers forming them. So there is also coincidence with 3, 6, 9 because numbers 4, 6, 8 also form three-membered arithmetical sequence with sum 18 and arithmetical mean 6. In addition, 4, 6, 8 are one-digit numbers. Similarly coincident date is 4.6.2018 (when I was diagnosed with F84.5, F42.2, F21 at the visit with the psychiatrist), which has sum of digits 21 and from digits different than 4, 6, 8 numbers 21 and 210 (2*3*5*7, product of four one-digit prime numbers) can be formed.

24.12.2018 I noticed that from the digits of GS 21, 42, 84 two three-membered arithmetical sequences can be formed: 2, 8, 14 and 4, 8, 12. These ASes can be formed by digits of GS 1, 2, 4, 8.
1, 2, 4, 8 is a four-membered geometrical sequence. It is non-constant and has four digits in it. That GS can be formed by some digits of GS 21, 42, 84 and by some digits in numbers in the date 24.12.2018.

Large coincidence can be found in numbers formed by two last digits in numbers forming the date 24.12.2018. These numbers are: 24, 12, 18. If they are sorted ascendingly, they form an AS: 12, 18, 24. Sums of digits in numbers forming AS 12, 18, 24 are: 3, 9, 6, if they are sorted ascendingly, they form "Tesla's arithmetical sequence" (TAS) - 3, 6, 9!

1. Middle term in the sequence 12, 18, 24 is 18.
2. Arithmetic mean of the AS 12, 18, 24 is 18 ((12+18+24):3 = 54:3 = 18).
3. Sum of digits in numbers forming 12, 18, 24 is 18 (1+2+1+8+2+4 = 18).
4. Sum of products of digits in numbers forming 12, 18, 24 is 18: 1*2 + 1*8 + 2*4 = 2+8+8 = 18.

The GS 12, 18, 24 is very coincident with sum of numbers and digits in TAS - 18. It may be the only non-constant sequence which has the same arithmetical mean, sum of digits and sum of products (or only digits which are present in the numbers) of digits in numbers forming the sequence. Another example of such a sequence is constant 0,0,0.

The common difference of 12, 18, 24 is 6 - the same as CD of 6, 12, 18, which was also coincident because 6.12.2018 I noticed that product of digits in the AS 11, 15, 19 is the same as sum of numbers forimng that sequence. 6 is arithmetical mean and middle term of TAS. Both 6, 12, 18 and 11, 15, 18 have the same sum of digits - 18, the same as in the case of TAS.

There are 9 days between 6.12.2018 and 15.12.2018 and 9 days between 15.12.2018 and 24.12.2018. There are 18 days between 6.12.2018 and 24.12.2018.