1Math::NumSeq::LuckyNumbUesresr(3C)ontributed Perl DocumeMnattaht:i:oNnumSeq::LuckyNumbers(3)
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NAME

6       Math::NumSeq::LuckyNumbers -- sieved out multiples by the sequence
7       itself
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SYNOPSIS

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

15       This is the so-called "Lucky" numbers obtained by sieving out multiples
16       taken from the sequence itself
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18           starting i=1
19           1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, ...
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21       The sieve begins with the odd numbers
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23           1,3,5,7,9,11,13,15,17,19,21,23,25,...
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25       Then sieve[2]=3 from the sequence means remove every third number,
26       counting from the start, so remove 5,11,17, etc to leave
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28           1,3,7,9,13,15,19,21,25,...
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30       Then the next value sieve[3]=7 means remove every seventh number, so 19
31       etc, to leave
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33           1,3,7,9,13,15,21,25,...
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35       Then sieve[4]=9 means remove every ninth from what remains, and so on.
36       In each case the removals count from the start of the values which
37       remain at that stage.
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39       It can be shown the values grow at roughly the same rate as the primes,
40       i =~ value/log(value).
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FUNCTIONS

43       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
44       classes.
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46       "$seq = Math::NumSeq::LuckyNumbers->new ()"
47           Create and return a new sequence object.
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49       "$i = $seq->value_to_i_estimate($value)"
50           Return an estimate of the i corresponding to $value.  It can be
51           shown that values grow roughly at the same rate as the primes,
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53               i ~= value/log(value)
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55           So "value_to_i_estimate()" returns "$value/log($value)".
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SEE ALSO

58       Math::NumSeq, Math::NumSeq::ReRound, Math::NumSeq::ReReplace
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HOME PAGE

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

64       Copyright 2012, 2013, 2014, 2016, 2019 Kevin Ryde
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66       Math-NumSeq is free software; you can redistribute it and/or modify it
67       under the terms of the GNU General Public License as published by the
68       Free Software Foundation; either version 3, or (at your option) any
69       later version.
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71       Math-NumSeq is distributed in the hope that it will be useful, but
72       WITHOUT ANY WARRANTY; without even the implied warranty of
73       MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
74       General Public License for more details.
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76       You should have received a copy of the GNU General Public License along
77       with Math-NumSeq.  If not, see <http://www.gnu.org/licenses/>.
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81perl v5.32.1                      2021-01-27     Math::NumSeq::LuckyNumbers(3)
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