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A014950
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Numbers n such that n divides 10^n - 1.
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8
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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; internal format)
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OFFSET
| 1,2
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COMMENTS
| Also, n such that n | R(n)=A002275(n). - Lekraj Beedassy (blekraj(AT)yahoo.com), Mar 25 2005
For n>1, 3 divides a(n).
Contribution from Farideh Firoozbakht (mymontain(AT)yahoo.com), Apr 14 2010: (Start)
We can easily show that if n is in the sequence and d divides n then for each positive integer k, d^k*n is in the sequence.
So we deduce that if n is in the sequence then for each positive integer k, n^k is in the sequence. In particular, 3^k is in this sequence for all k.
(End)
Numbers n such that n divides s(n), where s(1)=1, s(k)=s(k-1)+k*10^(k-1).
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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.
C. Cooper & R. E. Kennedy, "Niven Repunits and 10^n = 1 (mod n)" in 'The Fibonacci Quarterly' pp. 139-143 vol 27.2 May 1989, The Fibonacci Association,Aurora SD.
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FORMULA
| Solutions to 10^n=1 (mod n). - Vladeta Jovovic
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MATHEMATICA
| Select[Range[10000], PowerMod[10, #, #] == 1 &]
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CROSSREFS
| Cf. A122787.
Cf. A127100. [From Farideh Firoozbakht (mymontain(AT)yahoo.com), Apr 14 2010]
Sequence in context: A057262 A057232 A036145 * A036143 A006521 A014953
Adjacent sequences: A014947 A014948 A014949 * A014951 A014952 A014953
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KEYWORD
| nonn
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 18 2001
More terms from Larry Reeves (larryr(AT)acm.org), Jan 06 2005
Edited by Max Alekseyev (maxale(AT)gmail.com), May 20 2011
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