A341532 The number of even prime gaps g, satisfying g == 4 (mod 6), out of the first 2^n even prime gaps.

0, 0, 1, 3, 5, 11, 22, 41, 83, 169, 319, 627, 1223, 2445, 4868, 9638, 19118, 37967, 75256, 149528, 297561, 592031, 1178762, 2348333, 4679404, 9326903, 18596997, 37086109, 73967841, 147557809, 294406741, 587477778, 1172420817, 2340067090, 4671002562

Offset

0,4

Comments

It seems that the fraction of prime gaps g, satisfying g == 4 (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

Martin Ehrenstein, Table of n, a(n) for n = 0..43

Formula

a(n) = 2^n - A340948(n) - A341531(n).

Prog

(PARI) a(n) = my(vp=primes(2^n+2)); #select(x->((x%6)==4), vector(#vp-1, k, vp[k+1]-vp[k])); \\ Michel Marcus, Feb 16 2021

Crossrefs

Cf. A001223, A340948, A341531.

Sequence in context: A283818 A352006 A004039 * A293338 A168655 A005830

Adjacent sequences: A341529 A341530 A341531 * A341533 A341534 A341535

Keyword

nonn

Author

A.H.M. Smeets, Feb 13 2021

Extensions

a(29) and beyond from Martin Ehrenstein, Mar 01 2021

Status

approved