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%I
%S 2,5,3,3,3,13,11,17,71,29,89,103,61,31,131,151,31,173,59,199,71,31,73,
%T 229,61,271,293,151,101,103,89,181,127,197,397,137,103,431,439,149,
%U 467,131,263,181,283,293,599,619,317,367,769,257,197,263,809,271,821,167,61,433,179,449
%N Primes of the form n/(p(n+1)-p(n)), where p(n)=n-th prime.
%C Entries may be repeated and are shown in order of increasing generator n.
%e n=8: 8/(p(8+1)-p(8))=8/(23-19)=2=a(1).
%e n=10: 10/(p(10+1)-p(10))=10/(31-29)=5=a(2).
%e n=12: 12/(p(12+1)-p(12))=12/(41-37)=3=a(3).
%e n=18: 18/(p(18+1)-p(18))=18/(67-61)=3=a(4).
%e n=24: 24/(p(24+1)-p(24))=24/(97-89)=3=a(5).
%e n=26: 26/(p(26+1)-p(26))=26/(103-101)=13=a(6),
%t With[{nn=3000},Select[#[[1]]/#[[2]]&/@Thread[{Range[nn-1],#[[2]]-#[[1]]&/@ Partition[Prime[Range[nn]],2,1]}],PrimeQ]] (* _Harvey P. Dale_, Apr 13 2015 *)
%Y Cf. A000040.
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Sep 12 2008
%E Corrected and extended by _R. J. Mathar_, Sep 26 2008
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