

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
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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



FORMULA

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



KEYWORD

nonn,more


AUTHOR



STATUS

approved



