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%I #5 Mar 30 2012 18:40:03
%S 0,1,4,14,5,3,11,52,54,34,27,45,18,84,61,160,147,444,647,47,311,33,
%T 851,224,82,41,216,148,728,89,3357,57,659,3853,1814,504,920,1222,2019,
%U 4256
%N Distances between the locations of new prime gaps (A014320).
%C A014320 lists "new" gaps in the sequence A001223 of prime gaps (not necessarily records as A005669 does).
%C The locations of these new gaps in A001223 are 1, 2, 4, 9, 24, 30, 34,...
%C 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.
%C 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...
%p A001223 := proc(n) option remember; ithprime(n+1)-ithprime(n) ; end proc:
%p 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:
%p 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:
%p A131702 := proc(n) locng(n+1)-locng(n)-1 ; end proc: seq(A131702(n),n=1..40) ;
%Y Cf. A001223.
%K nonn
%O 1,3
%A _Giovanni Teofilatto_, Sep 16 2007
%E More terms, program and comment by _R. J. Mathar_, Aug 23 2010
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