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A145202
Primes of form 4*n^2 + 4*n + 653.
4
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
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
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Oct 04 2008
STATUS
approved