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 A141637 Primes of the form n/(p(n+1)-p(n)), where p(n)=n-th prime. 0

%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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Last modified March 27 18:55 EDT 2023. Contains 361575 sequences. (Running on oeis4.)