A131702 Distances between the locations of new prime gaps (A014320).

0, 1, 4, 14, 5, 3, 11, 52, 54, 34, 27, 45, 18, 84, 61, 160, 147, 444, 647, 47, 311, 33, 851, 224, 82, 41, 216, 148, 728, 89, 3357, 57, 659, 3853, 1814, 504, 920, 1222, 2019, 4256

Offset: 1

Author

Giovanni Teofilatto, Sep 16 2007

Keywords

• nonn

Comments

A014320 lists "new" gaps in the sequence A001223 of prime gaps (not necessarily records as A005669 does).

The locations of these new gaps in A001223 are 1, 2, 4, 9, 24, 30, 34,...

The present sequence lists the first difference of these locations, minus 1: a(1) = 2-1-1. a(2)=4-2-1. a(3)=9-4-1. a(4)=24-9-1.

The sequence therefore argues: need to skip 0 in A001223 to reach a new gap, need to skip 1 to reach a new gap, need to skip 4 to reach a new gap...

Crossrefs

Cf. A001223.

Programs

Maple

A001223 := proc(n) option remember; ithprime(n+1)-ithprime(n) ; end proc:
A014320 := proc(n) option remember; if n = 1 then return 1; else for k from 1 do t := A001223(k) ; isn := true; for i from 1 to n-1 do if procname(i) = t then isn := false; end if; end do: if isn then return t; end if; end do: end if; end proc:
locng := proc(n) option remember; g := A014320(n) ; for k from 1 do if A001223(k) = g then return k; end if; end do: end proc:
A131702 := proc(n) locng(n+1)-locng(n)-1 ; end proc: seq(A131702(n),n=1..40) ;

Extensions

More terms, program and comment by R. J. Mathar, Aug 23 2010