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

1,1

Comments

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

Links

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

Example

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.

Mathematica

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

Crossrefs

Subsequence of A014601.

Sequence in context: A131559 A366783 A051211 * A309197 A076683 A045542

Adjacent sequences: A105170 A105171 A105172 * A105174 A105175 A105176

Keyword

nonn

Author

Pierre CAMI, Apr 11 2005

Extensions

More terms from Amiram Eldar, Jul 18 2021

Status

approved