1Math::NumSeq::PrimeIndeUxsOerrdeCro(n3t)ributed Perl DocMuamtehn:t:aNtuimoSneq::PrimeIndexOrder(3)
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NAME

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

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

15       This is the order of primeness by Neil Fernandez, counting levels of
16       prime at prime index iterations,
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18           <http://www.borve.org/primeness/FOP.html>
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20           i     = 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17
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22           value = 0, 1, 2, 0, 3, 0, 1, 0, 0, 0, 4, 0, 1, 0, 0, 0, 2, ...
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24       Any composite has order 0.  The order for a prime is based on whether
25       its index in the list of all primes 2,3,5,7,11,etc is a prime and how
26       many times that prime index descent can be repeated.
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28       For example i=17 is a prime and is at index 7 in the list of all
29       primes.  That index 7 is a prime too and is at index 4.  Then stop
30       there since 4 is not a prime.  Two iterations to reach a non-prime
31       means i=17 has value 2 as its order of primeness.
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33   Primes Only
34       Option "on_values => 'primes'" selects the orders of just the primes
35       2,3,5,7,etc.  The effect is to eliminate the 0s from the sequence.
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37           1, 2, 3, 1, 4, 1, 2, 1, 1, 1, 5, 1, 2, 1, 1, 1, ...
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FUNCTIONS

40       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
41       classes.
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43       "$seq = Math::NumSeq::PrimeIndexOrder->new (level => $n)"
44           Create and return a new sequence object.
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SEE ALSO

47       Math::NumSeq, Math::NumSeq::Primes, Math::NumSeq::PrimeIndexPrimes,
48       Math::NumSeq::ErdosSelfridgeClass
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HOME PAGE

51       <http://user42.tuxfamily.org/math-numseq/index.html>
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LICENSE

54       Copyright 2011, 2012, 2013, 2014, 2016, 2019, 2020 Kevin Ryde
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56       Math-NumSeq is free software; you can redistribute it and/or modify it
57       under the terms of the GNU General Public License as published by the
58       Free Software Foundation; either version 3, or (at your option) any
59       later version.
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61       Math-NumSeq is distributed in the hope that it will be useful, but
62       WITHOUT ANY WARRANTY; without even the implied warranty of
63       MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
64       General Public License for more details.
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66       You should have received a copy of the GNU General Public License along
67       with Math-NumSeq.  If not, see <http://www.gnu.org/licenses/>.
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71perl v5.36.0                      2023-01-20  Math::NumSeq::PrimeIndexOrder(3)
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