login
A341531
The number of even prime gaps g satisfying g == 2 (mod 6) out of the first 2^n even prime gaps.
8
1, 2, 3, 4, 7, 13, 23, 43, 85, 170, 320, 628, 1224, 2446, 4869, 9640, 19119, 37969, 75258, 149530, 297562, 592033, 1178763, 2348334, 4679406, 9326904, 18596999, 37086110, 73967842, 147557811, 294406743, 587477780, 1172420818, 2340067092, 4671002564
OFFSET
0,2
COMMENTS
It seems that the fraction of prime gaps g, satisfying g == 2 (mod 6), tends to a constant, say c, when the number of prime gaps tends to infinity. From n = 28 we obtain that c < 0.276, while it can be argued heuristically that c > 0.25.
LINKS
FORMULA
a(n) = 2^n - A340948(n) - A341532(n).
PROG
(PARI) a(n) = my(vp=primes(2^n+2)); #select(x->((x%6)==2), vector(#vp-1, k, vp[k+1]-vp[k])); \\ Michel Marcus, Feb 16 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
A.H.M. Smeets, Feb 13 2021
EXTENSIONS
a(29) and beyond from Martin Ehrenstein, Mar 01 2021
STATUS
approved