

A014950


Numbers n such that n divides 10^n  1.


19



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
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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(k1) + k*10^(k1).
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. 139143, 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

Olivier Gérard


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



