A290541 Record gaps between numbers that are either prime or twice a prime.

1, 3, 6, 10, 11, 12, 13, 15, 19, 21, 25, 28, 35, 40, 48, 57, 60, 64, 70, 75, 83, 90, 95, 117, 120, 144, 148, 150, 153, 167, 168, 196, 205, 212, 214, 221, 234, 244, 254, 255

Offset

1,2

Comments

Records in A290496.

The gap of 57 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

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

Formula

a(n) = A290489(n) - A290488(n).

Example

a(3) = 6 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

With[{nn = 10^7}, Union@ FoldList[Max, Differences@ #] &@ Union@ Flatten@ {#, 2 TakeWhile[#, # < Prime[nn]/2 &]} &@ Prime@ Range@ nn] (* Michael De Vlieger, Aug 06 2017 *)

Crossrefs

Cf. A001751, A290488, A290489, A290496.

Sequence in context: A307574 A169911 A073851 * A043321 A241858 A231668

Adjacent sequences: A290538 A290539 A290540 * A290542 A290543 A290544

Keyword

more,nonn

Author

Bobby Jacobs, Aug 05 2017

Extensions

a(36)-a(40) from Giovanni Resta, Aug 06 2017

Status

approved