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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A100249 A138477 A182240

Adjacent sequences:  A346773 A346774 A346775 * A346777 A346778 A346779

KEYWORD

nonn,more

AUTHOR

A.H.M. Smeets, Aug 03 2021

STATUS

approved

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Last modified October 16 16:20 EDT 2021. Contains 348042 sequences. (Running on oeis4.)