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

1,2

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

Links

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A285375 A321372 A001948 * A325113 A328393 A189529

Adjacent sequences: A121909 A121910 A121911 * A121913 A121914 A121915

Keyword

nonn

Author

Zak Seidov, Sep 02 2006

Status

approved