%I #14 Sep 08 2022 08:45:01

%S 0,1,2,3,5,6,7,9,13,16,17,18,19,20,24,28,36,37,39,40,41,42,45,49,50,

%T 51,53,57,58,60,61,62,64,69,70,71,73,74,75,79,83,85,91,92,93,95,100,

%U 101,108,112,113,116,118,125,129,134,136,139,144

%N Numbers n where 36n^2+36n+11 is prime.

%C 36m^2+36m+11=(6m+3)^2+2, i.e. two more than the square of odd multiples of 3. 36m^2+36m+11=72*(m*(m+1)/2)+11, i.e. eleven more than seventy-two times triangular numbers.

%H Vincenzo Librandi, <a href="/A056900/b056900.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) =A002024((A056899(n+2)-11)/72)

%F a(n) = A091199(n+1) - 1. - _Jeppe Stig Nielsen_, May 14 2017

%e a(3)=3 because 36*3^2+36*3+11=443 which is prime

%t lst={};Do[If[PrimeQ[36*n^2+36*n+11],AppendTo[lst,n]],{n,0,100}];lst (* _Vincenzo Librandi_, Jul 14 2012 *)

%t Select[Range[0,200],PrimeQ[36#^2+36#+11]&] (* _Harvey P. Dale_, Sep 19 2020 *)

%o (Magma) [n: n in [0..200]| IsPrime(36*n^2+36*n+11)]; // _Vincenzo Librandi_, Jul 14 2012

%Y This sequence (with the formula above) generates all except the first two terms of the sequence of primes of the form k^2+2, A056899.

%Y Cf. A091199.

%K nonn,easy

%O 0,3

%A _Henry Bottomley_, Jul 05 2000