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A144103 Let N(p,i) denote the result of applying "nextprime" i times to p; a(n) = smallest prime p such that N(p,2) - p = 2*n, or -1 if no such prime exists.

%I A144103 #73 May 19 2024 22:44:15
%S A144103 -1,3,5,23,19,47,83,211,109,317,619,199,1373,1123,1627,4751,2557,3413,
%T A144103 4289,1321,2161,2477,7963,5591,9551,17239,15823,14087,19603,34963,
%U A144103 36389,33223,24251,35603,43321,19609,134507,31393,136999,31397,38461,107357
%N A144103 Let N(p,i) denote the result of applying "nextprime" i times to p; a(n) = smallest prime p such that N(p,2) - p = 2*n, or -1 if no such prime exists.
%C A144103 p and p+2n are primes and there is one prime in the range p+1 to p+2n-1.
%C A144103 a(n) is the prime for which 2n+2 first occurs in A031131.
%H A144103 Martin Raab, <a href="/A144103/b144103.txt">Table of n, a(n) for n = 1..469</a> (terms 1..342 from Robert G. Wilson v)
%H A144103 Mersenne Forum, <a href="https://www.mersenneforum.org/showthread.php?t=27301">Gaps between non-consecutive primes</a>
%t A144103 nn=51; t=Table[0,{nn}]; t[[1]]=-1; cnt=1; n=1; While[cnt<nn, n++; d=(Prime[n+2]-Prime[n])/2; If[d<=nn && t[[d]]==0, cnt++; t[[d]]=Prime[n]]]; t=Rest[t]
%t A144103 Flatten[Table[Select[Partition[Prime[Range[20000]],3,1],#[[3]]-#[[1]] == 2n+2&,1],{n,41}],1][[All,1]] (* _Harvey P. Dale_, Jun 26 2017 *)
%Y A144103 Cf. A031131.
%Y A144103 A000230 is an analogous sequence based on N(p,1). - _N. J. A. Sloane_, Nov 07 2020
%K A144103 sign
%O A144103 1,2
%A A144103 _T. D. Noe_, Sep 11 2008
%E A144103 Definition edited by _N. J. A. Sloane_, Nov 07 2020