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A341532 The number of even prime gaps g, satisfying g == 4 (mod 6), out of the first 2^n even prime gaps. 6
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 (list; graph; refs; listen; history; text; internal format)
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: A283603 A283818 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

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Last modified July 29 12:56 EDT 2021. Contains 346346 sequences. (Running on oeis4.)