login
Primes of the form (2*p^2 + 1)/3 where p is a prime > 3.
0

%I #17 May 18 2023 19:42:34

%S 17,113,193,241,353,641,1873,3361,5281,8513,10753,16433,17713,18593,

%T 21841,25873,34961,80273,92753,107201,111521,117041,134401,158113,

%U 168673,172721,182353,195121,211313,217361,221953,239201,279073,376001,394241

%N Primes of the form (2*p^2 + 1)/3 where p is a prime > 3.

%C The corresponding p values are the odd terms of A175256.

%F a(n) = (2*A175255(n+1)+1)/3.

%e 17 is a term since for p=5, (2*p^2 + 1)/3 = (2*5^2 + 1)/3 = 17 and 17 is prime.

%t Select[(2*Prime[Range[3, 140]]^2 + 1)/3, PrimeQ] (* _Amiram Eldar_, May 18 2023 *)

%o (PARI) forprime(p=5, 1000, my(Ap=floor((2*p^2+1)/3)); if(isprime(Ap), print1(Ap,", ")))

%Y Cf. A175255, A175256.

%K nonn

%O 1,1

%A _Alain Rocchelli_, Apr 11 2023