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A163418
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Primes of the form ((p-1)/2)^2+((p+1)/2), where p is prime.
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13
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3, 7, 13, 31, 43, 73, 211, 241, 421, 463, 1123, 1723, 2551, 2971, 4831, 5701, 6163, 8011, 8191, 9901, 11131, 12433, 14281, 17293, 19183, 20023, 23563, 24181, 28393, 30103, 31153, 35911, 37831, 43891, 46441, 53593, 60271, 77563, 83233, 86143
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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((3-1)/2)^2+((3+1)/2)=1+2=3;
((5-1)/2)^2+((5+1)/2)=4+3=7;
((7-1)/2)^2+((7+1)/2)=9+4=13,..
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MATHEMATICA
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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
Select[((#-1)/2)^2+((#+1)/2)&/@Prime[Range[200]], PrimeQ] (* Harvey P. Dale, Aug 06 2012 *)
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PROG
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(PARI) forprime(p=3, 10^3, if(isprime(q=((p-1)/2)^2+(p+1)/2), print1(q, ", "))) \\ Derek Orr, Apr 30 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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