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
Max Alekseyev, Table of n, a(n) for n = 1..438 (terms 1..364 from T. D. Noe)
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.
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 and Max Alekseyev, Smallest primitive factor of 10^n -1, or 0 if not yet found, for a(n) and n=1..10000
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
KEYWORD
nonn,base
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