A121912 - OEIS

%I #22 Feb 27 2019 09:45:39

%S 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,

%T 55,59,61,67,71,73,79,83,89,90,91,97,99,101,103,107,109,113,127,131,

%U 137,139,149,151,157,163,165,167,173,179,181,191,193,197,199,211,223,227

%N Numbers k such that 10^k == 10 (mod k).

%C By Fermat, all primes are members.

%C 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

%C 10^2^k + 1, 10^5^k + 1 and 10^10^k + 1 are terms for k >= 0. - _Jinyuan Wang_, Feb 11 2019

%H Robert Israel, <a href="/A121912/b121912.txt">Table of n, a(n) for n = 1..10000</a>

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

%p filter:= n -> (10 &^ n - 10 mod n = 0):

%p select(filter, [$1..1000]); # _Robert Israel_, Feb 10 2019

%t Select[Range[250], PowerMod[10, #, # ] == Mod[10, # ] &] (* _Ray Chandler_, Sep 02 2006 *)

%o (PARI) is(n) = Mod(10, n)^n == Mod(10, n) \\ _Jinyuan Wang_, Feb 11 2019

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

%K nonn

%O 1,2

%A _Zak Seidov_, Sep 02 2006