1Math::NumSeq::Pronic(3)User Contributed Perl DocumentatioMnath::NumSeq::Pronic(3)
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NAME

6       Math::NumSeq::Pronic -- pronic numbers
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SYNOPSIS

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

14       The pronic numbers i*(i+1),
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16           0, 2, 6, 12, 20, 30, ...
17           starting i=0
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19       These are twice the triangular numbers, and half way between the
20       perfect squares.
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FUNCTIONS

23       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
24       classes.
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26       "$seq = Math::NumSeq::Pronic->new ()"
27           Create and return a new sequence object.
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29   Iterating
30       "$seq->seek_to_i($i)"
31           Move the current sequence position to $i.  The next call to
32           "next()" will return $i and corresponding value.
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34       "$seq->seek_to_value($value)"
35           Move the current sequence position so that "next()" will give
36           $value on the next call, or if $value is not a pronic number then
37           the next pronic above $value.
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39   Random Access
40       "$value = $seq->ith($i)"
41           Return "$i*($i+1)".
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43       "$bool = $seq->pred($value)"
44           Return true if $value is a pronic number, ie. i*(i+1) for some i.
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46       "$i = $seq->value_to_i_ceil($value)"
47       "$i = $seq->value_to_i_floor($value)"
48           Return the $i index of $value, rounding up or down if $value is not
49           a pronic number.
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51       "$i = $seq->value_to_i_estimate($value)"
52           Return an estimate of the i corresponding to $value.  value=i*(i+1)
53           is inverted by
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55               $i = int( (sqrt(4*$value + 1) - 1)/2 )
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SEE ALSO

58       Math::NumSeq, Math::NumSeq::Squares, Math::NumSeq::Triangular
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HOME PAGE

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

64       Copyright 2010, 2011, 2012, 2013, 2014, 2016, 2017, 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 v5.34.0                      2021-07-22           Math::NumSeq::Pronic(3)
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