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%I #8 Jun 18 2017 11:50:31
%S 2,2,3,2,7,5,7,17,23,29,19,41,11,17,37,41,31,101,17,53,113,59,41,127,
%T 43,13,11,139,29,157,89,61,37,103,109,113,239,251,137,101,61,307,313,
%U 337,373,127,101,137,419,113,457,461,239,479,167,103,181,139,47,193,101,107,653
%N Primes of the form n/(p(n)-p(n-1)), where p(n)=n-th prime.
%C Entries may be repeated and are shown in order of increasing generator n.
%H Harvey P. Dale, <a href="/A141652/b141652.txt">Table of n, a(n) for n = 1..1000</a>
%e n=2: 2/(p(2)-p(2-1))=2/(3-2)=2=a(1).
%e n=4: 4/(p(4)-p(4-1))=4/(7-5)=2=a(2).
%e n=6: 6/(p(6)-p(6-1))=6/(13-11)=3=a(3).
%e n=12: 12/(p(12)-p(12-1))=12/(37-31)=2=a(4).
%e n=14: 14/(p(14)-p(14-1))=14/(43-41)=7=a(5).
%e n=20: 20/(p(20)-p(20-1))=20/(71-67)=5=a(6).
%e n=28: 28/(p(28)-p(28-1))=28/(107-103)=7=a(7),
%t Select[Table[n/(Prime[n]-Prime[n-1]),{n,2,2500}],PrimeQ] (* _Harvey P. Dale_, Jan 23 2013 *)
%t With[{nn=3000},Select[#[[1]]/#[[2]]&/@Thread[{Range[2,nn],Abs[ Differences[ Prime[Range[nn]]]]}],PrimeQ]] (* _Harvey P. Dale_, Jun 18 2017 *)
%Y Cf. A000040.
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Sep 13 2008
%E Corrected and extended by _R. J. Mathar_, Sep 26 2008
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