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

3, 11, 37, 101, 41, 271, 7, 13, 239, 4649, 73, 137, 333667, 9091, 21649, 513239, 9901, 53, 79, 265371653, 909091, 31, 2906161, 17, 5882353, 2071723, 5363222357, 19, 52579, 1111111111111111111, 3541, 27961, 43, 1933, 10838689, 23, 4093

Offset

1,1

Comments

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

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

References

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

Links

Rows n=1..352, flattened

David Eugene Smith and Yoshio Mikami, A History of Japanese Mathematics, Open Court, Chicago, 1914; chapter X.

Eric Weisstein's World of Mathematics, Decimal Expansion.

Index entries for sequences related to decimal expansion of 1/n

Example

First rows of irregular triangle are:
3;
11;
37;
101;
41, 271;
7, 13;
239, 4649;
73, 137;
333667;
9091;
21649, 513239;
9901;
53, 79, 265371653;
909091;
31, 2906161;
17, 5882353;
...

Mathematica

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 *)

Crossrefs

Cf. A007138 (first column).

Sequence in context: A095088 A306362 A007138 * A243110 A061075 A005422

Adjacent sequences: A046104 A046105 A046106 * A046108 A046109 A046110

Keyword

nonn,tabf,base

Author

Eric W. Weisstein

Extensions

First 276 rows in b-file from T. D. Noe, Jun 01 2010

Rows n=277..322 in b-file from Ray Chandler, May 01 2017

Rows n=323..352 in b-file from Max Alekseyev, Apr 26 2022

Status

approved