A217755 Numbers n such that ((n^2 + n)/2)^2 + 1 is prime.

1, 3, 4, 8, 11, 15, 20, 24, 28, 31, 39, 43, 48, 64, 75, 76, 79, 80, 111, 116, 120, 135, 148, 155, 160, 168, 179, 184, 200, 203, 208, 211, 216, 223, 224, 235, 243, 251, 263, 264, 288, 303, 319, 320, 324, 348, 351, 356, 364, 371, 375, 388, 416, 419, 420, 424, 428, 439, 443, 451, 456, 459

Offset: 1

Author

Luca Brigada Villa, Mar 26 2013

Keywords

• nonn

Comments

Also, numbers n such that the sum of the first n cubes precedes a prime.

Examples

			1 is in the sequence because ((1^2 + 1)/2)^2 + 1 = 2 and 2 is prime;
3 is in the sequence because ((3^2 + 3)/2)^2 + 1 = 37 and 37 is prime.
		

Crossrefs

Cf. A067186.

Programs

Magma

[n: n in [1..500] | IsPrime(s+1) where s is (n^2+n)^2 div 4]; // Bruno Berselli, Mar 27 2013

Mathematica

Select[Range[400], PrimeQ[((#^2 + #)/2)^2 + 1] &] (* Alonso del Arte, Mar 26 2013 *)

PARI

for(n=1,10^3, if(isprime(((n^2 + n)/2)^2 + 1), print1(n,", "))); /* Joerg Arndt, Mar 27 2013 */