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

%I A121912 #22 Feb 27 2019 09:45:39
%S A121912 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 A121912 55,59,61,67,71,73,79,83,89,90,91,97,99,101,103,107,109,113,127,131,
%U A121912 137,139,149,151,157,163,165,167,173,179,181,191,193,197,199,211,223,227
%N A121912 Numbers k such that 10^k == 10 (mod k).
%C A121912 By Fermat, all primes are members.
%C A121912 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 A121912 10^2^k + 1, 10^5^k + 1 and 10^10^k + 1 are terms for k >= 0. - _Jinyuan Wang_, Feb 11 2019
%H A121912 Robert Israel, <a href="/A121912/b121912.txt">Table of n, a(n) for n = 1..10000</a>
%e A121912 13 is a term because 10^13 = 13*769230769230 + 10.
%p A121912 filter:= n -> (10 &^ n - 10 mod n = 0):
%p A121912 select(filter, [$1..1000]); # _Robert Israel_, Feb 10 2019
%t A121912 Select[Range[250], PowerMod[10, #, # ] == Mod[10, # ] &] (* _Ray Chandler_, Sep 02 2006 *)
%o A121912 (PARI) is(n) = Mod(10, n)^n == Mod(10, n) \\ _Jinyuan Wang_, Feb 11 2019
%Y A121912 Cf. A056969 (10^n modulo n), A121014 (Nonprime terms in A121912).
%K A121912 nonn
%O A121912 1,2
%A A121912 _Zak Seidov_, Sep 02 2006