Math::NumSeq::Pronic -- pronic numbers
use Math::NumSeq::Pronic; my $seq = Math::NumSeq::Pronic->new; my ($i, $value) = $seq->next;
The pronic numbers i*(i+1),
0, 2, 6, 12, 20, 30, ... starting i=0
These are twice the triangular numbers, and half way between the perfect squares.
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
$seq = Math::NumSeq::Pronic->new ()
Create and return a new sequence object.
Move the current sequence position to
$i. The next call to
next() will return
$i and corresponding value.
Move the current sequence position so that
next() will give
$value on the next call, or if
$value is not a pronic number then the next pronic above
$value = $seq->ith($i)
$bool = $seq->pred($value)
Return true if
$value is a pronic number, ie. i*(i+1) for some i.
$i = $seq->value_to_i_ceil($value)
$i = $seq->value_to_i_floor($value)
$i index of
$value, rounding up or down if
$value is not a pronic number.
$i = $seq->value_to_i_estimate($value)
Return an estimate of the i corresponding to
$value. value=i*(i+1) is inverted by
$i = int( (sqrt(4*$value + 1) - 1)/2 )
Copyright 2010, 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.
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