A163588 - OEIS

%I #21 Feb 16 2025 22:37:21

%S 2,3,5,17,37,101,197,257,401,577,677,1297,1601,2917,3137,4357,5477,

%T 7057,8101,8837,12101,13457,14401,15377,15877,16901,17957,21317,22501,

%U 24337,25601,28901,30977,32401,33857,41617,42437,44101,50177,52901,55697,57601,62501

%N Primes which are within 1 of a square number.

%C 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

%H David A. Corneth, <a href="/A163588/b163588.txt">Table of n, a(n) for n = 1..10000</a> (First 1000 terms from G. C. Greubel)

%F {3} Union A002496. - _R. J. Mathar_, Aug 06 2009

%e 6^2 + 1 = 37, which is prime, so 37 is in the sequence.

%e 8^2 + 1 = 65 = 5 * 13, so 65 is not in the sequence.

%t Union[{3}, Select[Range[100]^2 + 1, PrimeQ]] (* _G. C. Greubel_, Jul 28 2017 *)

%Y Cf. A002496, A002522.

%K nonn,easy

%O 1,1

%A _Gaurav Kumar_, Jul 31 2009