A346776 a(n) is the number of consecutive even prime gaps (g1, g2) satisfying g1 == 2 (mod 6) and g2 == 0 (mod 6) out of the first 2^n consecutive even prime gaps.

0, 0, 0, 0, 2, 3, 6, 15, 28, 58, 132, 254, 515, 1042, 2088, 4172, 8337, 16720, 33556, 66948, 134088, 268037, 535435, 1069932, 2139357, 4275948, 8544351, 17076036

Offset

0,5

Comments

The prime gaps are given in A001223. Here look at terms of A001223 satisfying the conditions A001223(k) == 2 and A001223(k+1) == 0 (mod 6) for 1 < k <= 2^n + 1.

Links

Table of n, a(n) for n=0..27.

Formula

a(n) = A341531(n) - A346777(n) - 1.

a(n) - A345334(n) is in {0, 1}. This holds not only for powers of 2 counts, but for all counts.

Example

The sequence A001223(n) mod 6 is given by: 1, 2, 2, 4, 2, 4, 2, 4, 0, 2, 0, 4, 2, 4, 0, 0, 2, 0, 4, 2, 0, 4, 0, 2, ..., denoted here as b(0), b(1), b(2), ..., i.e. b(n) = A001223(n+1) (mod 6) for n >= 0.
The term b(0) is excluded by definition. The conditions b(k) = 2 and b(k+1) == 0 are obtained for k = 9, 16, 19, ...
So a(n) = 0 for n <= 3 (the first value of k is 9, i.e. larger than 2^3), and a(4) = 2 (two values of k satisfying k <= 2^4).

Crossrefs

Cf. A001223, A340948, A341531, A341532, A345332, A345333, A345334, A346777.

Sequence in context: A255353 A248652 A158027 * A371570 A100249 A138477

Adjacent sequences: A346773 A346774 A346775 * A346777 A346778 A346779

Keyword

nonn,more

Author

A.H.M. Smeets, Aug 03 2021

Status

approved