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

1,1

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

Links

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

Formula

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

Example

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.

Mathematica

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

Crossrefs

Cf. A002496, A002522.

Sequence in context: A118958 A259596 A189536 * A270539 A053182 A348153

Adjacent sequences: A163585 A163586 A163587 * A163589 A163590 A163591

Keyword

nonn,easy

Author

Gaurav Kumar, Jul 31 2009

Status

approved