1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
|
#!/usr/bin/perl -w
# Copyright 2011, 2012, 2013, 2015, 2018, 2020 Kevin Ryde
# This file is part of Math-PlanePath.
#
# Math-PlanePath 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-PlanePath 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-PlanePath. If not, see <http://www.gnu.org/licenses/>.
use 5.004;
use strict;
use Test;
plan tests => 9;
use lib 't','xt';
use MyTestHelpers;
BEGIN { MyTestHelpers::nowarnings(); }
use MyOEIS;
use Math::PlanePath::FractionsTree;
# GP-DEFINE read("my-oeis.gp");
#------------------------------------------------------------------------------
# A093873 -- Kepler numerators
# starting from 1/1 is duplicate tree halves, so repeat each row
# 1
# -
# 1
#
# 1 1 i/(i+j) and j/(i+j)
# - -
# 2 2
#
# 1 2 1 2
# - - - -
# 3 3 3 3
#
# 1 3 2 3 1 3 2 3
# - - - - - - - -
# 4 4 5 5 4 4 5 5
#
# 1 4 3 4 2 5 3 5 1 4 3 4 2 5 3
# - - - - - - - - - - - - - - -
# 5 5 7 7 7 7 8 8 5 5 7 7 7 7 8
# 1
# / \
# 1 1 i/(i+j) and j/(i+j)
# / \ / \
# 1 2 1 2
# / \ / \ / \ / \
# 1 3 2 3 1 3 2 3
# 1/1
# 1/2 1/2
# 1/3 2/3 1/3 2/3
# 1/4 3/4 2/5 3/4 1/4 3/4 2/5 3/5
# GP-DEFINE A093873_pq(n) = {
# GP-DEFINE my(p=1,q=1);
# GP-DEFINE forstep(i=logint(n,2)-1,0,-1,
# GP-DEFINE [p,q] = [if(bittest(n,i),q,p), p+q]);
# GP-DEFINE [p,q];
# GP-DEFINE }
# GP-Test my(v=OEIS_samples("A093873")); /* OFFSET=1 */ \
# GP-Test vector(#v,n, A093873_pq(n)[1]) == v
# GP-Test my(v=OEIS_samples("A093875")); /* OFFSET=1 */ \
# GP-Test vector(#v,n, A093873_pq(n)[2]) == v
MyOEIS::compare_values
(anum => 'A093873',
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::FractionsTree->new (tree_type => 'Kepler');
my @got;
for (my $n = 1; @got < $count; $n++) {
my ($x,$y) = $path->n_to_xy(sans_second_highest_bit($n));
push @got, $x;
}
return \@got;
});
# denominators
MyOEIS::compare_values
(anum => 'A093875',
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::FractionsTree->new (tree_type => 'Kepler');
my @got = (1);
for (my $n = 2; @got < $count; $n++) {
my ($x,$y) = $path->n_to_xy(sans_second_highest_bit($n));
push @got, $y;
}
return \@got;
});
sub sans_second_highest_bit {
my ($n) = @_;
my $h = high_bit($n);
$h >>= 1;
return $h + ($n & ($h-1));
}
ok (sans_second_highest_bit(7), 3);
ok (sans_second_highest_bit(9), 5);
ok (sans_second_highest_bit(13), 5);
MyOEIS::compare_values
(anum => 'A162751',
name => 'sans_second_highest_bit()',
func => sub {
my ($count) = @_;
my @got;
for (my $n = 1; @got < $count; $n++) {
push @got, sans_second_highest_bit($n+1);
}
return \@got;
});
sub high_bit {
my ($n) = @_;
my $bit = 1;
while ($bit <= $n) { $bit <<= 1; }
return $bit >> 1;
}
MyOEIS::compare_values
(anum => 'A053644', # OFFSET=0
name => 'high_bit()',
func => sub {
my ($count) = @_;
my @got;
for (my $n = 0; @got < $count; $n++) {
push @got, high_bit($n);
}
return \@got;
});
#------------------------------------------------------------------------------
# A086593 -- Kepler half-tree denominators, every second value
MyOEIS::compare_values
(anum => 'A086593',
name => 'Kepler half-tree denominators every second value',
func => sub {
my ($count) = @_;
my @got;
my $path = Math::PlanePath::FractionsTree->new (tree_type => 'Kepler');
for (my $n = $path->n_start; @got < $count; $n += 2) {
my ($x, $y) = $path->n_to_xy ($n);
push @got, $y;
}
return \@got;
});
# is also the sum X+Y, skipping initial 2
MyOEIS::compare_values
(anum => q{A086593},
name => 'as sum X+Y',
func => sub {
my ($count) = @_;
my $path = Math::PlanePath::FractionsTree->new (tree_type => 'Kepler');
my @got = (2);
for (my $n = $path->n_start; @got < $count; $n++) {
my ($x, $y) = $path->n_to_xy ($n);
push @got, $x+$y;
}
return \@got;
});
#------------------------------------------------------------------------------
exit 0;
|
