|
%I #34 Apr 26 2022 20:47:26
%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 <a href="/A046107/b046107.txt">Rows n=1..352, flattened</a>
%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_
%E First 276 rows in b-file from _T. D. Noe_, Jun 01 2010
%E Rows n=277..322 in b-file from _Ray Chandler_, May 01 2017
%E Rows n=323..352 in b-file from _Max Alekseyev_, Apr 26 2022
|
