OFFSET
1,1
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
LINKS
R. J. Mathar, Table of n, a(n) for n = 1..7999
FORMULA
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
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Definition rewritten by Bruno Berselli, Oct 15 2012
Mathematica updated by Jean-François Alcover, Jun 19 2013
STATUS
approved