Kevin Ryde > Math-NumSeq-71 > Math::NumSeq::PrimeIndexOrder

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Module Version: 71   Source  

NAME ^

Math::NumSeq::PrimeIndexOrder -- order of primeness by primes at prime indexes

SYNOPSIS ^

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

DESCRIPTION ^

This is the order of primeness by Neil Fernandez, counting levels of prime at prime index iterations,

http://www.borve.org/primeness/FOP.html

    i     = 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17

    value = 0, 1, 2, 0, 3, 0, 1, 0, 0, 0, 4, 0, 1, 0, 0, 0, 2, ...

Any composite has order 0. The order for a prime is based on whether its index in the list of all primes 2,3,5,7,11,etc is a prime and how many times that prime index descent can be repeated.

For example i=17 is a prime and is at index 7 in the list of all primes. That index 7 is a prime too and is at index 4. Then stop there since 4 is not a prime. Two iterations to reach a non-prime means i=17 has value 2 as its order of primeness.

Primes Only

Option on_values => 'primes' selects the orders of just the primes 2,3,5,7,etc. The effect is to eliminate the 0s from the sequence.

    1, 2, 3, 1, 4, 1, 2, 1, 1, 1, 5, 1, 2, 1, 1, 1, ...

FUNCTIONS ^

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

$seq = Math::NumSeq::PrimeIndexOrder->new (level => $n)

Create and return a new sequence object.

SEE ALSO ^

Math::NumSeq, Math::NumSeq::Primes, Math::NumSeq::PrimeIndexPrimes, Math::NumSeq::ErdosSelfridgeClass

HOME PAGE ^

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

LICENSE ^

Copyright 2011, 2012, 2013, 2014 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/>.

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