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A046107 Triangle of prime numbers in which n-th row lists all primes p such that 1/p has decimal period n, n >= 1. 13

%I

%S 3,11,37,101,41,271,7,13,239,4649,73,137,333667,9091,21649,513239,

%T 9901,53,79,265371653,909091,31,2906161,17,5882353,2071723,5363222357,

%U 19,52579,1111111111111111111,3541,27961,43,1933,10838689,23,4093

%N Triangle of prime numbers in which n-th row lists all primes p such that 1/p has decimal period n, n >= 1.

%C The number of numbers in each row n is given by A112505(n).

%C In the 18th century, the Japanese mathematician Ajima Naonobu (aka Ajima Chokuyen) gave the terms through 5882353 (Smith and Mikami, p. 199). - _Jonathan Sondow_, May 25 2013

%D Ajima Naonobu (aka Ajima Chokuyen), Fujin Isshũ (Periods of Decimal Fractions).

%H Ray Chandler, <a href="/A046107/b046107.txt">Rows n=1..322, flattened</a> (first 276 rows from T. D. Noe)

%H David Eugene Smith and Yoshio Mikami, <a href="http://archive.org/details/historyofjapanes00smitiala">A History of Japanese Mathematics</a>, Open Court, Chicago, 1914; chapter X.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DecimalExpansion.html">Decimal Expansion.</a>

%H <a href="/index/1#1overn">Index entries for sequences related to decimal expansion of 1/n</a>

%e First rows of irregular triangle are:

%e 3;

%e 11;

%e 37;

%e 101;

%e 41, 271;

%e 7, 13;

%e 239, 4649;

%e 73, 137;

%e 333667;

%e 9091;

%e 21649, 513239;

%e 9901;

%e 53, 79, 265371653;

%e 909091;

%e 31, 2906161;

%e 17, 5882353;

%e ...

%t pp={}; Do[f=Transpose[FactorInteger[10^n-1]][[1]]; p=Complement[f, pp]; pp=Union[pp, p]; Print[p], {n, 66}] (* _T. D. Noe_, Sep 08 2005 *)

%Y Cf. A007138 (first column).

%K nonn,tabf,base

%O 1,1

%A _Eric W. Weisstein_

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Last modified June 4 17:50 EDT 2020. Contains 334828 sequences. (Running on oeis4.)