NAME

Math::NumSeq::LongFractionPrimes -- primes for which fraction 1/p has a long period

SYNOPSIS

 use Math::NumSeq::LongFractionPrimes;
 my $seq = Math::NumSeq::LongFractionPrimes->new;
 my ($i, $value) = $seq->next;

DESCRIPTION

In progress ...

This is the primes for which fraction 1/p written out in decimal has digits repeating in period p-1.

    starting i=1 for prime=2
    2, 3, 7, 17, 19, 23, 29, 47, 59, 61, 97, 109, 113, 131, ...

For example 1/7=0.142857142857142857... is runs of 7-1=6 repeating digits "142857", so 7 is in the sequence. On the other hand 1/11=0.09090909... is only 2 repeating digits, so is not in the sequence.

A prime p has full period p-1 digits when the base 10 is a primitive root modulo p, meaning that 10 mod p, 100 mod p, 1000 mod p, ..., 10^(p-2) mod p, are all != 1.

Radix

An optional radix parameter selects a base other than decimal.

If radix is a square, 4,9,16,etc then only primes 2 and 3 have period p-1 and the sequence stops after them.

FUNCTIONS

See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.

$seq = Math::NumSeq::LongFractionPrimes->new ()

Create and return a new sequence object.

$value = $seq->pred($value)

Return true if $value is a prime and fraction 1/p has digit period p-1.

$i = $seq->i_start ()

Return 1, the first term in the sequence being at i=1.

SEE ALSO

Math::NumSeq, Math::NumSeq::Primes

HOME PAGE

http://user42.tuxfamily.org/math-numseq/index.html

LICENSE

Copyright 2012 Kevin Ryde

Math-NumSeq is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.

Math-NumSeq is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with Math-NumSeq. If not, see <http://www.gnu.org/licenses/>.