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A163418 Primes of the form ((p-1)/2)^2+((p+1)/2), where p is prime.

%I A163418 #17 Dec 22 2016 23:15:57
%S A163418 3,7,13,31,43,73,211,241,421,463,1123,1723,2551,2971,4831,5701,6163,
%T A163418 8011,8191,9901,11131,12433,14281,17293,19183,20023,23563,24181,28393,
%U A163418 30103,31153,35911,37831,43891,46441,53593,60271,77563,83233,86143
%N A163418 Primes of the form ((p-1)/2)^2+((p+1)/2), where p is prime.
%C A163418 Subsequence of A002383. - _Charles R Greathouse IV_, Aug 11 2009
%H A163418 G. C. Greubel, <a href="/A163418/b163418.txt">Table of n, a(n) for n = 1..1500</a>
%e A163418 ((3-1)/2)^2+((3+1)/2)=1+2=3;
%e A163418 ((5-1)/2)^2+((5+1)/2)=4+3=7;
%e A163418 ((7-1)/2)^2+((7+1)/2)=9+4=13,..
%t A163418 f[n_]:=((p-1)/2)^2+((p+1)/2); lst={};Do[p=Prime[n];If[PrimeQ[f[p]],AppendTo[lst,f[p]]],{n,6!}];lst
%t A163418 Select[((#-1)/2)^2+((#+1)/2)&/@Prime[Range[200]],PrimeQ] (* _Harvey P. Dale_, Aug 06 2012 *)
%o A163418 (PARI) forprime(p=3,10^3,if(isprime(q=((p-1)/2)^2+(p+1)/2),print1(q,", "))) \\ _Derek Orr_, Apr 30 2015
%Y A163418 Cf. A162652.
%K A163418 nonn,easy
%O A163418 1,1
%A A163418 _Vladimir Joseph Stephan Orlovsky_, Jul 27 2009