A290488 Lower ends of record gaps between numbers that are either prime or twice a prime.

2, 7, 47, 181, 467, 526, 1069, 1262, 1327, 2477, 3274, 5119, 12854, 20809, 28229, 31397, 338038, 520462, 546391, 1050631, 1761206, 1964987, 3466943, 6084986, 27348829, 27915754, 111108769, 113652443, 230126378, 231902267, 327764081, 438981007, 581755318, 1837981547, 2489382697

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

Robert G. Wilson v, Table of n, a(n) for n = 1..37

Formula

a(n) = A290489(n) - A290541(n).

Example

a(3) = 47 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

nxt[n_] := Block[{k = n +1}, While[ !PrimeQ[ k] && ! PrimeQ[ k/2], k++]; k]; p = 2; q = 3; mx = 0; lst = {}; While[p < 2500000000, If[q > mx + p, mx = q - p; AppendTo[ lst, p]]; p = q; q = nxt@ q]; lst (* Robert G. Wilson v, Aug 03 2017 *)

Crossrefs

Cf. A001751, A290489, A290541.

Sequence in context: A201481 A054555 A072287 * A276649 A091117 A056854

Adjacent sequences: A290485 A290486 A290487 * A290489 A290490 A290491

Keyword

nonn

Author

Bobby Jacobs, Aug 03 2017

Extensions

a(11) onward from Robert G. Wilson v, Aug 03 2017

Status

approved