cp's OEIS Frontend

A117012 Primes of the form n^2+5*n+c (n>=0), where c=3 for even n and c=-3 for odd n.

%I A117012 #13 Aug 25 2025 02:54:35
%S A117012 3,17,47,107,173,269,503,641,809,983,1187,1637,2441,2753,4157,4547,
%T A117012 4967,5393,5849,6311,6803,7829,8363,9497,11981,12653,13331,14753,
%U A117012 15497,17027,22943,26723,29753,31859,32933,38609,39791,42221,47297,49943,58313
%N A117012 Primes of the form n^2+5*n+c (n>=0), where c=3 for even n and c=-3 for odd n.
%D A117012 Harvey Cohn, Advanced Number Theory,Dover, New York, 1962, page 155.
%H A117012 Robert Israel, <a href="/A117012/b117012.txt">Table of n, a(n) for n = 1..10000</a>
%p A117012 select(isprime, [seq(n^2 + 5*n + (-1)^n * 3, n=1..1000)]); # _Robert Israel_, Aug 25 2025
%t A117012 f[n_] := If[Mod[n, 2] == 1, n^2 + 5*n - 3, n^2 + 5*n + 3] b = Flatten[Table[If[PrimeQ[f[n]] == True, f[n], {}], {n, 1, 100}]]
%o A117012 (PARI) for(n=1, 250, k=n^2+5*n+3-6*(n%2); if(isprime(k), print1(k,", ")))
%Y A117012 Cf. A014209, A082605.
%K A117012 nonn,changed
%O A117012 1,1
%A A117012 _Roger L. Bagula_, Apr 16 2006
%E A117012 Edited and extended by _N. J. A. Sloane_, Apr 17 2006