A121912 Numbers k such that 10^k == 10 (mod k).

1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 15, 17, 18, 19, 23, 29, 30, 31, 33, 37, 41, 43, 45, 47, 53, 55, 59, 61, 67, 71, 73, 79, 83, 89, 90, 91, 97, 99, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 165, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227

Offset: 1

Author

Zak Seidov, Sep 02 2006

Keywords

• nonn

Comments

By Fermat, all primes are members.

Numbers k not divisible by 4 or 25 such that the multiplicative order of 10 mod (k/gcd(k,10)) divides k-1. - Robert Israel, Feb 10 2019

10^2^k + 1, 10^5^k + 1 and 10^10^k + 1 are terms for k >= 0. - Jinyuan Wang, Feb 11 2019

Examples

			13 is a term because 10^13 = 13*769230769230 + 10.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A056969 (10^n modulo n), A121014 (Nonprime terms in A121912).

Programs

Maple

filter:= n -> (10 &^ n - 10 mod n = 0):
select(filter, [$1..1000]); # Robert Israel, Feb 10 2019

Mathematica

Select[Range[250], PowerMod[10, #, # ] == Mod[10, # ] &] (* Ray Chandler, Sep 02 2006 *)

PARI

is(n) = Mod(10, n)^n == Mod(10, n) \\ Jinyuan Wang, Feb 11 2019