A066506 Least k > n^2 such that (k^3+1)/(n^2+1) is an integer.

3, 9, 19, 33, 43, 48, 99, 69, 163, 201, 197, 289, 339, 393, 451, 513, 579, 374, 411, 801, 543, 644, 1059, 791, 725, 1353, 739, 1244, 863, 1801, 1063, 2049, 1699, 1245, 1905, 1663, 2739, 2889, 3043, 3201, 3363, 3529, 2099, 2383, 4051, 2783, 3059, 4609, 2973, 3525

Offset

1,1

Links

Table of n, a(n) for n=1..50.

Formula

a(n) = 2*n^2 + 1 for n = 1, 2, 3, 4, 7, 9, 10, 12, 13, 14, 15, 16, 17, 20, 23, 26, ...

Prog

(PARI) a(n) = {my(d=n^2+1); for(k=d, oo, if((k^3+1)%d==0, return(k))); } \\ Jinyuan Wang, Apr 05 2020

Crossrefs

Sequence in context: A194139 A194115 A226184 * A058331 A328950 A049749

Adjacent sequences: A066503 A066504 A066505 * A066507 A066508 A066509

Keyword

nonn

Author

Benoit Cloitre, Jan 04 2002

Extensions

Name clarified and more terms from Jinyuan Wang, Apr 05 2020

Status

approved