

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)


15



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
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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 p1.  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

T. D. Noe, Table of n, a(n) for n=1..500
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^n1.
Makoto Kamada, Factorizations of 11...11 (Repunit).
Yousuke Koide, Factors of Repunit Numbers.
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
Wikipedia, Repeating decimals
Robert G. Wilson v, Smallest primitive factor of 10^n 1, or 0 if not yet found, for a(n) and n=1..10000
Index entries for sequences related to decimal expansion of 1/n


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^n1) 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
Adjacent sequences: A007135 A007136 A007137 * A007139 A007140 A007141


KEYWORD

nonn,base


AUTHOR

N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v, Jud McCranie


STATUS

approved



