A015951 Numbers k such that k | 5^k + 1.

1, 2, 3, 9, 21, 26, 27, 63, 81, 147, 189, 243, 338, 441, 567, 609, 729, 903, 1029, 1323, 1378, 1701, 1827, 2187, 2667, 2709, 3087, 3969, 4263, 4394, 4401, 5103, 5481, 6321, 6561, 7203, 8001, 8127, 9261, 9429, 11907, 12789, 13149, 13203

Offset: 1

Author

Robert G. Wilson v

Keywords

• nonn

Links

• Jinyuan Wang, Table of n, a(n) for n = 1..5000 (first 500 terms from Seiichi Manyama)

Crossrefs

5^k+m is divisible by k: A123062 (m=2), A123052 (m=3), A123047 (m=4).

Column k=5 of A333429.

Programs

Magma

[n: n in [1..10^5] | Modexp(5, n, n)+1 eq n]; // Jinyuan Wang, Dec 29 2018

Mathematica

Select[Range@ 14000, Divisible[5^# + 1, #] &] (* Michael De Vlieger, Oct 10 2016 *)
Select[Range[15000],PowerMod[5,#,#]==#-1&] (* Harvey P. Dale, Aug 11 2024 *)

PARI

isok(n) = Mod(5, n)^n == -1; \\ Michel Marcus, Oct 11 2016

Python

for n in range(1,10**5):
    if pow(5,n,n)+1 == n: print(n, end=', ') # Stefano Spezia, Dec 30 2018