A056900 Numbers n where 36n^2+36n+11 is prime.

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, 51, 53, 57, 58, 60, 61, 62, 64, 69, 70, 71, 73, 74, 75, 79, 83, 85, 91, 92, 93, 95, 100, 101, 108, 112, 113, 116, 118, 125, 129, 134, 136, 139, 144

Offset: 0

Author

Henry Bottomley, Jul 05 2000

Keywords

• nonn
• easy

Comments

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.

Examples

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

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.

Cf. A091199.

Programs

Magma

[n: n in [0..200]| IsPrime(36*n^2+36*n+11)]; // Vincenzo Librandi, Jul 14 2012

Mathematica

lst={};Do[If[PrimeQ[36*n^2+36*n+11],AppendTo[lst,n]],{n,0,100}];lst (* Vincenzo Librandi, Jul 14 2012 *)
Select[Range[0,200],PrimeQ[36#^2+36#+11]&] (* Harvey P. Dale, Sep 19 2020 *)

Formula

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

a(n) = A091199(n+1) - 1. - Jeppe Stig Nielsen, May 14 2017