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

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

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 27 2009

Keywords

• nonn
• easy

Comments

Subsequence of A002383. - Charles R Greathouse IV, Aug 11 2009

Examples

			((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,..
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1500

Crossrefs

Cf. A162652.

Programs

Mathematica

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 *)

PARI

forprime(p=3,10^3,if(isprime(q=((p-1)/2)^2+(p+1)/2),print1(q,", "))) \\ Derek Orr, Apr 30 2015