A105173 Numbers k such that either k*(k+1)/4 + 1 or k*(k+1)/4 - 1 or both are primes.

3, 7, 8, 15, 16, 23, 24, 32, 39, 40, 47, 48, 55, 56, 63, 64, 71, 79, 80, 87, 95, 103, 104, 111, 112, 119, 120, 128, 135, 136, 143, 151, 152, 159, 167, 175, 176, 183, 199, 208, 216, 223, 224, 231, 232, 239, 240, 247, 248, 255, 256, 263, 264, 271, 279, 287, 288

Offset: 1

Author

Pierre CAMI, Apr 11 2005

Keywords

• nonn

Comments

The primes are (sum of numbers from 1 to k)/2 + or - 1.

Examples

			3*4/4 = 3, 3-1 = 2 is prime so a(1) = 3.
7*8/4 = 14, 14-1 = 13 is prime so a(2) = 7.
8*9/4 = 18, 18-1 = 17 is prime, 18+1 = 19 is prime, so a(3) = 8.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A014601.

Programs

Mathematica

Select[Range[300], Or @@ PrimeQ[#*(#+1)/4 + {-1, 1}] &] (* Amiram Eldar, Jul 18 2021 *)

Extensions

More terms from Amiram Eldar, Jul 18 2021