A154419 Primes of the form 20*k^2 + 36*k + 17.

17, 73, 953, 1249, 2377, 2833, 3329, 4441, 8737, 12401, 13417, 15569, 17881, 20353, 21649, 28729, 33457, 36809, 49801, 51817, 62497, 67049, 71761, 74177, 86857, 89513, 100537, 103393, 118273, 121369, 127681, 134153, 144161, 161641, 168913

Offset: 1

Author

Vincenzo Librandi, Jan 09 2009

Keywords

• nonn
• easy

Comments

Also primes of the form 5*j^2 + 18*j + 17. (Proof: this format implies that j=2*k, even, because otherwise 5*j^2 + 18*j + 17 is even and cannot be prime. So 5*j^2 + 18*j + 17 = 20*k^2 + 36*k + 17.) - R. J. Mathar, Jan 12 2009

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A017377, A154418.

Programs

Magma

[a: n in [0..100] | IsPrime(a) where a is 20*n^2+36*n+17]; // Vincenzo Librandi, Jul 23 2012

Mathematica

Select[Table[20n^2+36n+17,{n,0,6001}],PrimeQ] (* Vincenzo Librandi, Jul 23 2012 *)

PARI

select(isprime, vector(100, n, 20*(n-1)^2 + 36*(n-1) + 17)) \\ Robert C. Lyons,  Feb 27 2025