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

1,1

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.

Links

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

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A001751, A290488, A290541.

Sequence in context: A363209 A052446 A362062 * A002873 A309910 A042171

Adjacent sequences: A290486 A290487 A290488 * A290490 A290491 A290492

Keyword

nonn

Author

Bobby Jacobs, Aug 03 2017

Extensions

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

Status

approved