A123047 Numbers k that divide 5^k + 4.

1, 3, 129, 60767, 76433163, 454034821, 26675718567, 164304369911289

Offset: 1

Author

Alexander Adamchuk, Nov 04 2006

Keywords

• hard
• more
• nonn

Comments

k must be odd since any power of 5 plus 4 is odd. - Robert G. Wilson v, Nov 14 2006

a(9) > 10^15. - Max Alekseyev, Oct 17 2016

Large term (may not be the next one): 3014733401203184049549. - Max Alekseyev, Oct 18 2013

Crossrefs

Solutions to 5^n == k (mod n): A067946 (k=1), A015951 (k=-1), A124246 (k=2), A123062 (k=-2), A123061 (k=3), A123052 (k=-3), A125949 (k=4), this sequence (k=-4), A123091 (k=5), A015891 (k=-5), A277350 (k=6), A277348 (k=-6).

Programs

Mathematica

Do[ If[ PowerMod[5, 2n - 1, 2n - 1] + 5 == 2n, Print[2n - 1]], {n, 10^9}] (* Robert G. Wilson v *)

PARI

is(n)=Mod(5,n)^n==-4 \\ Charles R Greathouse IV, Nov 04 2016

Extensions

a(4) and a(5) from Robert G. Wilson v, Nov 14 2006

a(7) from Ryan Propper, Mar 23 2007

a(8) from Max Alekseyev, Oct 17 2016