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A007138 Smallest primitive factor of 10^n - 1. Also smallest prime p such that 1/p has repeating decimal expansion of period n.
(Formerly M2888)
22
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)
OFFSET
1,1
COMMENTS
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
REFERENCES
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).
LINKS
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
Torbjörn Granlund, Factors of 10^n-1.
David Eugene Smith and Yoshio Mikami, A History of Japanese Mathematics, Open Court, Chicago, 1914; chapter X.
S. S. Wagstaff, Jr., The Cunningham Project
Eric Weisstein's World of Mathematics, Decimal Expansion
EXAMPLE
a(3) = 37 since 1/37 = 0.027027... has period 3, and 37 is the smallest such prime (in fact, the only one).
MAPLE
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:
seq(A[n], n=1..60); # Robert Israel, Nov 10 2014
CROSSREFS
Cf. A046107.
Cf. A001913.
Sequence in context: A108544 A095088 A306362 * A046107 A243110 A061075
KEYWORD
nonn,base
AUTHOR
EXTENSIONS
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
STATUS
approved

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)