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A121912 Numbers k such that 10^k == 10 (mod k). 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 27 11:55 EST 2020. Contains 332305 sequences. (Running on oeis4.)