

A290489


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


5



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
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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: A013201 A309885 A052446 * 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



