%I #5 Jul 11 2012 17:15:11
%S 3,2,3,7,5,2,5,11,17,7,17,59,13,17,41,23,29,61,47,199,101,71,41,23,
%T 263,269,137,139,97,59,101,103,67,173,353,127,409,139,419,449,229,163,
%U 199,103,223,229,349,181,733,751,853,883,109,197,1033,347,521,211,137,1109,373
%N Primes of the form n/(2*(p(n-1)-p(n-2))), where p(n)=n-th prime.
%e n=12: 12/(2*(p(12-1)-p(12-2)))=12/(2*(31-29))=3=a(1).
%e n=16: 16/(2*(p(16-1)-p(16-2)))=16/(2*(47-43))=2=a(2).
%e n=24: 24/(2*(p(24-1)-p(24-2)))=24/(2*(83-79))=3=a(3).
%e n=28: 28/(2*(p(28-1)-p(28-2)))=28/(2*(103-101))=7=a(4).
%e n=40: 40/(2*(p(40-1)-p(40-2)))=40/(2*(167-163))=5=a(5).
%t Select[Table[n/(2(Prime[n-1]-Prime[n-2])),{n,3,5000}],PrimeQ] (* _Harvey P. Dale_, Jul 11 2012 *)
%Y Cf. A000040, A001223.
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, Sep 15 2008
%E Corrected and extended by _R. J. Mathar_, Sep 26 2008
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