%I #19 Aug 15 2024 06:21:42

%S 0,2,4,5,7,9,14,19,22,24,29,30,34,40,42,44,50,59,62,70,72,74,75,79,80,

%T 82,84,95,102,110,119,125,132,135,139,149,150,157,160,165,172,180,197,

%U 199,200,209,210,212,224,225,227,229,230,232,235,240,244,249

%N Numbers k such that 36*k^2 + 36*k + 13 is prime.

%C 36*k^2 + 36*k + 13 = (6*k+3)^2 + 4, which is 4 more than a square.

%H Vincenzo Librandi, <a href="/A056908/b056908.txt">Table of n, a(n) for n = 1..1000</a>

%e a(2)=4 since 36*4^2 + 36*4 + 13 = 733, which is prime (as well as being four more than a square).

%t Select[Range[0,700],PrimeQ[36#^2+36#+13]&] (* _Vincenzo Librandi_, Jul 14 2012 *)

%o (Magma) [n: n in [0..70]| IsPrime(36*n^2+36*n+13)]; // _Vincenzo Librandi_, Jul 14 2012

%o (PARI) is(n)=isprime(36*n^2+36*n+13) \\ _Charles R Greathouse IV_, Mar 01 2017

%Y This sequence and formula, together with A056907 and its formula, generate all primes of the form k^2+4, i.e., A005473.

%Y Cf. A056900, A056902, A056904, A056906.

%K nonn,easy

%O 1,2

%A _Henry Bottomley_, Jul 07 2000