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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.

%I A046107 #40 Feb 16 2025 08:32:38
%S A046107 3,11,37,101,41,271,7,13,239,4649,73,137,333667,9091,21649,513239,
%T A046107 9901,53,79,265371653,909091,31,2906161,17,5882353,2071723,5363222357,
%U A046107 19,52579,1111111111111111111,3541,27961,43,1933,10838689,23,4093,8779,11111111111111111111111
%N A046107 Triangle of prime numbers in which n-th row lists all primes p such that 1/p has decimal period n, n >= 1.
%C A046107 The number of numbers in each row n is given by A112505(n).
%C A046107 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 A046107 Ajima Naonobu (aka Ajima Chokuyen), Fujin Isshũ (Periods of Decimal Fractions).
%H A046107 <a href="/A046107/b046107.txt">Rows n=1..352, flattened</a>
%H A046107 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 A046107 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DecimalExpansion.html">Decimal Expansion.</a>
%H A046107 <a href="/index/1#1overn">Index entries for sequences related to decimal expansion of 1/n</a>
%e A046107 First rows of irregular triangle are:
%e A046107        3;
%e A046107       11;
%e A046107       37;
%e A046107      101;
%e A046107       41,     271;
%e A046107        7,      13;
%e A046107      239,    4649;
%e A046107       73,     137;
%e A046107   333667;
%e A046107     9091;
%e A046107    21649,  513239;
%e A046107     9901;
%e A046107       53,      79, 265371653;
%e A046107   909091;
%e A046107       31, 2906161;
%e A046107       17, 5882353;
%e A046107   ...
%t A046107 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 A046107 Cf. A007138 (first column), A061075 (last row elements).
%K A046107 nonn,tabf,base
%O A046107 1,1
%A A046107 _Eric W. Weisstein_
%E A046107 First 276 rows in b-file from _T. D. Noe_, Jun 01 2010
%E A046107 Rows n=277..322 in b-file from _Ray Chandler_, May 01 2017
%E A046107 Rows n=323..352 in b-file from _Max Alekseyev_, Apr 26 2022