1Math::NumSeq::Pronic(3)User Contributed Perl DocumentatioMnath::NumSeq::Pronic(3)
2
3
4
6 Math::NumSeq::Pronic -- pronic numbers
7
9 use Math::NumSeq::Pronic;
10 my $seq = Math::NumSeq::Pronic->new;
11 my ($i, $value) = $seq->next;
12
14 The pronic numbers i*(i+1),
15
16 0, 2, 6, 12, 20, 30, ...
17 starting i=0
18
19 These are twice the triangular numbers, and half way between the
20 perfect squares.
21
23 See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
24 classes.
25
26 "$seq = Math::NumSeq::Pronic->new ()"
27 Create and return a new sequence object.
28
29 Iterating
30 "$seq->seek_to_i($i)"
31 Move the current sequence position to $i. The next call to
32 "next()" will return $i and corresponding value.
33
34 "$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 $value.
38
39 Random Access
40 "$value = $seq->ith($i)"
41 Return "$i*($i+1)".
42
43 "$bool = $seq->pred($value)"
44 Return true if $value is a pronic number, ie. i*(i+1) for some i.
45
46 "$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 $value is not
49 a pronic number.
50
51 "$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
54
55 $i = int( (sqrt(4*$value + 1) - 1)/2 )
56
58 Math::NumSeq, Math::NumSeq::Squares, Math::NumSeq::Triangular
59
61 <http://user42.tuxfamily.org/math-numseq/index.html>
62
64 Copyright 2010, 2011, 2012, 2013, 2014, 2016, 2017, 2019 Kevin Ryde
65
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.
70
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.
75
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/>.
78
79
80
81perl v5.32.0 2020-07-28 Math::NumSeq::Pronic(3)