A145202 Primes of form 4*n^2 + 4*n + 653.

653, 661, 677, 701, 733, 773, 821, 877, 941, 1013, 1093, 1181, 1277, 1381, 1493, 1613, 1741, 1877, 2333, 2677, 2861, 3253, 3461, 3677, 4133, 4373, 4621, 4877, 5413, 5693, 5981, 6277, 6581, 7213, 7541, 7877, 8221, 8573, 8933, 9677, 10061, 10453, 10853

Offset: 1

Author

Klaus Brockhaus, Oct 04 2008

Keywords

• nonn

Comments

First 18 terms are for n from 0 through 17, next terms are for n = 20, 22, 23, 25, 26, 27, 29, 30, 31, 32, 34, 35, 36, 37, 38, 40, ...

The sequence of n such that 4*n^2 + 4*n + 653 is composite starts 18, 19, 21, 24, 28, 33, 39, 46, 54, 60, 61, 62, 63, 65, 67, 72, 73, 75, 81, 82, 84, 85, 86, 93, 95, 96, 100, ...

These primes are in A000414. [Bruno Berselli, Apr 20 2014]

Examples

			a(18) = 4*17^2 + 4*17 + 653 = 1877.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Prime-Generating Polynomial

Crossrefs

A145125 is essentially the same sequence.

Cf. A005846 (primes of form n^2 + n + 41).

Programs

Magma

[a: n in [0..100] | IsPrime(a) where a is  4*n^2 + 4*n + 653]; // Vincenzo Librandi, Apr 21 2014

Mathematica

Select[Table[4 n^2 + 4 n + 653, {n, 0, 100}], PrimeQ] (* Vincenzo Librandi, Apr 21 2014 *)

PARI

{for(n=0, 50, if(isprime(p=4*n^2+4*n+653), print1(p, ",")))}