A050265 - OEIS

%I #37 Sep 08 2022 08:44:58

%S 11,13,19,29,43,61,83,109,139,173,211,349,461,523,659,733,811,1069,

%T 1163,1579,1693,1811,1933,2749,3373,3539,3709,4243,4813,5011,5419,

%U 5843,7211,7699,7949,8461,9533,9811,10093,11261,13789,14461,15149,16573

%N Primes of the form 2*n^2 + 11.

%C The polynomial 2*n^2 + 11 first fails to produce a prime for n = 11, giving 253 = 11 * 23. - _Alonso del Arte_, Sep 04 2016

%C Let P(n) = 2*n^2 + 11. The polynomial P(2*n - 10) = 8*n^2 - 80*n + 11 produces prime values (not distinct) for n = 0 to 10. The polynomial P(3*n - 19) = 18*n^2 - 228*n + 733 produces distinct prime values for n = 0 to 9. - _Peter Bala_, Apr 16 2018

%H Vincenzo Librandi, <a href="/A050265/b050265.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-generating Polynomial.</a>

%F a(n) = 11 + 2*(A092968(n))^2. - _R. J. Mathar_, Jan 03 2009

%t Select[2Range[0, 100]^2 + 11, PrimeQ] (* _Harvey P. Dale_, May 20 2011 *)

%o (Magma) [a: n in [0..100] | IsPrime(a) where a is 2*n^2+11]; // _Vincenzo Librandi_, Dec 08 2011

%Y Cf. A005846, A007641.

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_

%E 11 added by _Vincenzo Librandi_, Dec 08 2011