A123061 Numbers k that divide 5^k - 3.

1, 2, 22, 77, 242, 371, 16102, 45727, 73447, 81286, 112277, 368237, 10191797, 13563742, 30958697, 389974222, 6171655457, 55606837682, 401469524477, 434715808966, 1729670231597, 12399384518278, 28370781933478, 32458602019394, 45360785149757, 1073804398767214

Offset: 1

Author

Alexander Adamchuk, Nov 04 2006

Keywords

• nonn

Comments

Some larger terms: 10157607413638637338691, 678641208236297002873422185407157785099272404809011007522511134591325167. - Max Alekseyev, Oct 20 2016

Crossrefs

Cf. A050259, A130422, A277554, A116629.

Solutions to 5^n == k (mod n): A067946 (k=1), A015951 (k=-1), A124246 (k=2), A123062 (k=-2), this sequence (k=3), A123052 (k=-3), A125949 (k=4), A123047 (k=-4), A123091 (k=5), A015891 (k=-5), A277350 (k=6), A277348 (k=-6).

Programs

Mathematica

Select[Range[1000000], IntegerQ[(PowerMod[5,#,# ]-3)/# ]&]
Do[If[IntegerQ[(PowerMod[5, n, n ]-3)/n], Print[n]], {n, 10^9}] (* Ryan Propper, Dec 30 2006 *)

PARI

is(n)=Mod(5,n)^n==3 \\ Charles R Greathouse IV, Nov 04 2016

Extensions

More terms from Farideh Firoozbakht, Nov 18 2006

Corrected and extended by Ryan Propper, Jan 01 2007

Entry revised by N. J. A. Sloane, Jan 24 2007

a(18) from Lars Blomberg, Dec 12 2011

a(19)-a(26) from Max Alekseyev, Oct 20 2016