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A007138
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Smallest primitive factor of 10^n - 1. Also smallest prime p such that 1/p has repeating decimal expansion of period n.
(Formerly M2888)
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22
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3, 11, 37, 101, 41, 7, 239, 73, 333667, 9091, 21649, 9901, 53, 909091, 31, 17, 2071723, 19, 1111111111111111111, 3541, 43, 23, 11111111111111111111111, 99990001, 21401, 859, 757, 29, 3191, 211, 2791, 353, 67, 103, 71, 999999000001
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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In the 18th century, the Japanese mathematician Ajima Naonobu (a.k.a. Ajima Chokuyen) gave the first 16 terms (Smith and Mikami, p. 199). - Jonathan Sondow, May 25 2013
Also the least prime number p such that the multiplicative order of 10 modulo p is n. - Robert G. Wilson v, Dec 09 2013
n always divides p-1. - Jon Perry, Nov 02 2014
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REFERENCES
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Ajima Naonobu (aka Ajima Chokuyen), Fujin Isshũ (Periods of Decimal Fractions).
J. Brillhart et al., Factorizations of b^n +/- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
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EXAMPLE
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a(3) = 37 since 1/37 = 0.027027... has period 3, and 37 is the smallest such prime (in fact, the only one).
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MAPLE
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S:= {}:
for n from 1 to 60 do
F:= numtheory:-factorset(10^n-1) minus S;
A[n]:= min(F);
S:= S union F;
od:
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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b-file truncated to 364 terms as a(365) was wrong and is currently unknown (pointed by Eric Chen), and a-file revised by Max Alekseyev, Apr 26 2022
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STATUS
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approved
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