A125775 Numbers k such that 5^k mod k = 5^k mod k^2.

1, 2, 4, 5, 6, 12, 25, 42, 52, 84, 125, 156, 186, 372, 625, 1092, 1218, 1302, 1806, 2436, 2604, 2756, 3125, 3612, 4836, 5334, 7212, 8268, 10668, 12324, 15625, 15918, 18858, 19140, 20771, 24492, 26080, 31668, 31836, 33852, 37716, 37758, 40487, 41542

Offset: 1

Author

Alexander Adamchuk, Dec 07 2006

Keywords

• nonn

Comments

Includes all powers of 5 (A000351).

a(2) = 2, a(4) = 5, a(35) = 20771 and a(43) = 40487 are the only listed primes. More known primes are listed in A123692.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000351, A123692, A068535, A125773, A125774.

Programs

Mathematica

Do[f=PowerMod[5,n,n];g=PowerMod[5,n,n^2];If[f==g,Print[n]],{n,1,1000000}]
Select[Range[42000],PowerMod[5,#,#]==PowerMod[5,#,#^2]&] (* Harvey P. Dale, Aug 20 2022 *)