NAME

Math::NumSeq::Pronic -- pronic numbers

SYNOPSIS

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

DESCRIPTION

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.

FUNCTIONS

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

$seq = Math::NumSeq::Pronic->new ()

Create and return a new sequence object.

Iterating

$seq->seek_to_i($i)

Move the current sequence position to $i. The next call to next() will return $i and corresponding value.

$seq->seek_to_value($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.

Random Access

$value = $seq->ith($i)

Return $i*($i+1).

$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)

Return the $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 )

SEE ALSO

Math::NumSeq, Math::NumSeq::Squares, Math::NumSeq::Triangular

HOME PAGE

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

LICENSE

Copyright 2010, 2011, 2012, 2013, 2014, 2016, 2017, 2019, 2020 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/>.