

A046107


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


15



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
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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



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^n1]][[1]]; p=Complement[f, pp]; pp=Union[pp, p]; Print[p], {n, 66}] (* T. D. Noe, Sep 08 2005 *)


CROSSREFS



KEYWORD

nonn,tabf,base


AUTHOR



EXTENSIONS

First 276 rows in bfile from T. D. Noe, Jun 01 2010


STATUS

approved



