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 A014950 Numbers n such that n divides 10^n - 1. 16
 1, 3, 9, 27, 81, 111, 243, 333, 729, 999, 2187, 2997, 4107, 6561, 8991, 12321, 13203, 19683, 20439, 26973, 36963, 39609, 59049, 61317, 80919, 110889, 118827, 151959, 177147, 183951, 242757, 332667, 356481, 455877, 488511, 531441, 551853, 728271 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also, n such that n | R(n) = A002275(n). - Lekraj Beedassy, Mar 25 2005 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 Numbers n such that n divides s(n), where s(1) = 1, s(k) = s(k-1) + k*10^(k-1). 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 Numbers n such that n divides A033713(n). - Hans Havermann, Jan 25 2014 REFERENCES 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. LINKS Hans Havermann and Robert G. Wilson v, Table of n, a(n) for n = 1..1600 (first 800 terms from Robert G. Wilson v) C. Cooper and R. E. Kennedy, Niven Repunits and 10^n = 1 (mod n), The Fibonacci Quarterly, pp. 139-143, vol 27, May 02 1989 Hans Havermann, A014950 factorized and atomized FORMULA Solutions to 10^n = 1 (mod n). - Vladeta Jovovic MATHEMATICA Select[ Range[3, 1000000, 6], PowerMod[10, #, #] == 1 &] (* modified by Robert G. Wilson v, Dec 03 2013 *) 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 *) PROG (PARI) is(n)=Mod(10, n)^n==1 \\ Charles R Greathouse IV, Nov 29 2013 CROSSREFS Cf. A066364, A114207, A122787, A127100, A232769. Sequence in context: A057262 A057232 A036145 * A271351 A036143 A248960 Adjacent sequences:  A014947 A014948 A014949 * A014951 A014952 A014953 KEYWORD nonn AUTHOR EXTENSIONS More terms from Vladeta Jovovic, Dec 18 2001 More terms from Larry Reeves (larryr(AT)acm.org), Jan 06 2005 Edited by Max Alekseyev, May 20 2011 STATUS approved

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Last modified March 25 12:11 EDT 2019. Contains 321470 sequences. (Running on oeis4.)