A049532 - OEIS (original) (raw)

7, 18, 32, 38, 41, 43, 57, 68, 70, 82, 93, 99, 107, 117, 118, 132, 143, 157, 168, 182, 193, 207, 218, 232, 239, 243, 251, 257, 268, 282, 293, 307, 318, 327, 332, 343, 357, 368, 378, 382, 393, 407, 408, 418, 432, 437, 443, 457, 468, 482, 493, 500, 507, 515

COMMENTS

The sequence is infinite. For instance, it contains all numbers of the form 7 + 25m. - Emmanuel Vantieghem, Oct 25 2016

More generally, the sequence contains all numbers of the form a(n) + (a(n)^2 + 1) * m for even a(n) and a(n) + (a(n)^2 + 1) * m / 2 for odd a(n). - David A. Corneth, Oct 25 2016

The asymptotic density of this sequence is 1 - A335963 = 0.1051587754... - Amiram Eldar, Jul 08 2020

EXAMPLE

a(1) = 7 because 7^2 + 1 = 49 + 1 = 50 is divisible by 25, a square.

MATHEMATICA

n=1; Reap[Do[While[SquareFreeQ[n^2+1], n++]; Sow[n]; n++, {c, 10000}]][[2, 1]] (* Zak Seidov, Feb 24 2011 *)

PROG

(PARI) for(n=1, 1e4, if(!issquarefree(n^2+1), print1(n", "))) \\ Charles R Greathouse IV, Feb 24 2011

(Magma) [n: n in [1..6*10^2]| not IsSquarefree(n^2+1)]; // Bruno Berselli, Oct 15 2012