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

3, 17, 47, 107, 173, 269, 503, 641, 809, 983, 1187, 1637, 2441, 2753, 4157, 4547, 4967, 5393, 5849, 6311, 6803, 7829, 8363, 9497, 11981, 12653, 13331, 14753, 15497, 17027, 22943, 26723, 29753, 31859, 32933, 38609, 39791, 42221, 47297, 49943, 58313

Offset: 1

Author

Roger L. Bagula, Apr 16 2006

Keywords

• nonn
• changed

References

• Harvey Cohn, Advanced Number Theory,Dover, New York, 1962, page 155.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A014209, A082605.

Programs

Maple

select(isprime, [seq(n^2 + 5*n + (-1)^n * 3, n=1..1000)]); # Robert Israel, Aug 25 2025

Mathematica

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}]]

PARI

for(n=1, 250, k=n^2+5*n+3-6*(n%2); if(isprime(k), print1(k,", ")))

Extensions

Edited and extended by N. J. A. Sloane, Apr 17 2006