A290489 Upper ends of record gaps between numbers that are either prime or twice a prime.

3, 10, 53, 191, 478, 538, 1082, 1277, 1346, 2498, 3299, 5147, 12889, 20849, 28277, 31454, 338098, 520526, 546461, 1050706, 1761289, 1965077, 3467038, 6085103, 27348949, 27915898, 111108917, 113652593, 230126531, 231902434, 327764249, 438981203, 581755523, 1837981759, 2489382911

Offset: 1

Author

Bobby Jacobs, Aug 03 2017

Keywords

• nonn

Comments

The gap between 31397 and 31454 is due to the record prime gap between 31397 and 31469 being almost exactly twice the record prime gap between 15683 and 15727.

Examples

			a(3) = 53 because the next number that is a prime or twice a prime after 47 is 53, and that is a record gap of size 6.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..40

Crossrefs

Cf. A001751, A290488, A290541.

Programs

Mathematica

p = op = 2; r = 0; Reap[While[p < 10^6, p++; If[PrimeQ[p] || PrimeQ[p/2], g = p - op; If[g > r, Sow@p; r = g]; op = p]]][[2, 1]] (* Giovanni Resta, Aug 04 2017 *)

Formula

a(n) = A290488(n) + A290541(n).

Extensions

a(17)-a(35) from Giovanni Resta, Aug 04 2017