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

Author

Bobby Jacobs, Aug 05 2017

Keywords

• more
• nonn

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.

Examples

			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.
		

Crossrefs

Cf. A001751, A290488, A290489, A290496.

Programs

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 *)

Formula

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

Extensions

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