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

1,1

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]

Links

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

Eric Weisstein's World of Mathematics, Prime-Generating Polynomial

Example

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

Mathematica

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

Prog

(PARI) {for(n=0, 50, if(isprime(p=4*n^2+4*n+653), print1(p, ", ")))}
(Magma) [a: n in [0..100] | IsPrime(a) where a is  4*n^2 + 4*n + 653]; // Vincenzo Librandi, Apr 21 2014

Crossrefs

A145125 is essentially the same sequence.

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

Sequence in context: A104823 A198170 A145125 * A188366 A255208 A060520

Adjacent sequences: A145199 A145200 A145201 * A145203 A145204 A145205

Keyword

nonn

Author

Klaus Brockhaus, Oct 04 2008

Status

approved