OFFSET
0,5
COMMENTS
It seems that the fraction of prime gaps g, satisfying g == 0 (mod 6), tends to a constant, say c, when the number of prime gaps tends to infinity. From n = 43 we obtain that c > 0.463, while it can be argued heuristically that c < 0.5.
LINKS
Martin Ehrenstein, Table of n, a(n) for n = 0..43
FORMULA
EXAMPLE
The first even prime gaps are given by 2, 2, 4, 2,..., A001223 without the leading 1.
The 8th even prime gap is the first gap satisfying g == 0 (mod 6), so a(3) = 1.
PROG
(PARI) a(n) = my(vp=primes(2^n+2)); #select(x->!(x%6), vector(#vp-1, k, vp[k+1]-vp[k])); \\ Michel Marcus, Feb 04 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
A.H.M. Smeets, Jan 31 2021
EXTENSIONS
a(26) corrected by Martin Ehrenstein, Feb 14 2021
a(29) and beyond from Martin Ehrenstein, Feb 18 2021
STATUS
approved