A163588 Primes which are within 1 of a square number.

2, 3, 5, 17, 37, 101, 197, 257, 401, 577, 677, 1297, 1601, 2917, 3137, 4357, 5477, 7057, 8101, 8837, 12101, 13457, 14401, 15377, 15877, 16901, 17957, 21317, 22501, 24337, 25601, 28901, 30977, 32401, 33857, 41617, 42437, 44101, 50177, 52901, 55697, 57601, 62501

Offset: 1

Author

Gaurav Kumar, Jul 31 2009

Keywords

• nonn
• easy

Comments

The only prime of the form n^2 - 1 is 3. Remember that n^2 - 1 = (n - 1)(n + 1), so, for example, for n = 12, we have n^2 - 1 = 143 = 11 * 13. - Alonso del Arte, Feb 16 2025

Examples

			6^2 + 1 = 37, which is prime, so 37 is in the sequence.
8^2 + 1 = 65 = 5 * 13, so 65 is not in the sequence.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000 (First 1000 terms from G. C. Greubel)

Crossrefs

Cf. A002496, A002522.

Programs

Mathematica

Union[{3}, Select[Range[100]^2 + 1, PrimeQ]] (* G. C. Greubel, Jul 28 2017 *)

Formula

{3} Union A002496. - R. J. Mathar, Aug 06 2009