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A014950
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Numbers m such that m divides 10^m - 1.
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26
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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
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OFFSET
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1,2
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COMMENTS
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For n > 1, 3 divides a(n). If m is in the sequence and d divides m then for each positive integer k, d^k*m is in the sequence. So if m is in the sequence then m^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 m such that m divides s(m), 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
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REFERENCES
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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.
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LINKS
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FORMULA
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MATHEMATICA
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Select[ Range[3, 1000000, 6], PowerMod[10, #, #] == 1 &] (* modified by Robert G. Wilson v, Dec 03 2013 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Jan 06 2005
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STATUS
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approved
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