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 A014950 Numbers n such that n divides 10^n - 1. 16

%I

%S 1,3,9,27,81,111,243,333,729,999,2187,2997,4107,6561,8991,12321,13203,

%T 19683,20439,26973,36963,39609,59049,61317,80919,110889,118827,151959,

%U 177147,183951,242757,332667,356481,455877,488511,531441,551853,728271

%N Numbers n such that n divides 10^n - 1.

%C Also, n such that n | R(n) = A002275(n). - _Lekraj Beedassy_, Mar 25 2005

%C For n > 1, 3 divides a(n). If n is in the sequence and d divides n then for each positive integer k, d^k*n is in the sequence. So if n is in the sequence then n^k is in the sequence for each positive integer k. In particular, 3^k is in this sequence for all k. - _Farideh Firoozbakht_, Apr 14 2010

%C Numbers n such that n divides s(n), where s(1) = 1, s(k) = s(k-1) + k*10^(k-1).

%C Number of terms <= 10^k, beginning with k = 0: 1, 3, 5, 10, 15, 25, 41, 68, 108, 178, 291, ..., . _Robert G. Wilson v_, Nov 30 2013

%C Numbers n such that n divides A033713(n). - _Hans Havermann_, Jan 25 2014

%D J. D. E. Konhauser et al., Which Way Did The Bicycle Go? Problem 80 pp. 26; 133, Dolciani Math. Exp., No. 18, MAA, Washington DC, 1996.

%H Hans Havermann and Robert G. Wilson v, <a href="/A014950/b014950.txt">Table of n, a(n) for n = 1..1600</a> (first 800 terms from Robert G. Wilson v)

%H C. Cooper and R. E. Kennedy, <a href="http://www.fq.math.ca/Scanned/27-2/kennedy.pdf">Niven Repunits and 10^n = 1 (mod n)</a>, The Fibonacci Quarterly, pp. 139-143, vol 27, May 02 1989

%H Hans Havermann, <a href="http://chesswanks.com/seq/a014950.txt">A014950 factorized and atomized</a>

%F Solutions to 10^n = 1 (mod n). - _Vladeta Jovovic_

%t Select[ Range[3, 1000000, 6], PowerMod[10, #, #] == 1 &] (* modified by _Robert G. Wilson v_, Dec 03 2013 *)

%t k = 3; A014950 = {1}; While[k < 1000000, If[ PowerMod[ 10, k, k] == 1, AppendTo[ A014950, k]; Print@ k]; k += 6]; A014950 (* _Robert G. Wilson v_, Nov 29 2013 *)

%o (PARI) is(n)=Mod(10,n)^n==1 \\ _Charles R Greathouse IV_, Nov 29 2013

%Y Cf. A066364, A114207, A122787, A127100, A232769.

%K nonn

%O 1,2