#!/usr/bin/perl -w
# Copyright 2012, 2013, 2014 Kevin Ryde
# This file is part of Math-NumSeq.
#
# 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/>.
# A046815, A083853.
use 5.004;
use strict;
use List::Util 'min','max';
use Test;
plan tests => 7;
use lib 't','xt';
use MyTestHelpers;
MyTestHelpers::nowarnings();
use MyOEIS;
use Math::NumSeq::FibonacciRepresentations;
# uncomment this to run the ### lines
# use Smart::Comments '###';
#------------------------------------------------------------------------------
# A000121 - R'(n), allowing Fib 1 twice
MyOEIS::compare_values
(anum => 'A000121',
# max_value => 2000000,
func => sub {
my ($count) = @_;
my @got;
my @seen;
my $seq = Math::NumSeq::FibonacciRepresentations->new;
my $prev = 0;
for (my $n = 1; @got < $count; $n++) {
my ($i, $value) = $seq->next;
push @got, $value + $prev;
$prev = $value;
}
$got[0] = 1;
return \@got;
});
#------------------------------------------------------------------------------
# A046815 - smallest x for which R(x) = n and x uses only even Fibs
MyOEIS::compare_values
(anum => 'A046815',
# max_value => 2000000,
func => sub {
my ($count) = @_;
require Math::NumSeq::Fibbinary;
my $fibbinary = Math::NumSeq::Fibbinary->new;
my $seq = Math::NumSeq::FibonacciRepresentations->new;
my @got;
my @seen;
for (my $n = 1; @got < $count; $n++) {
while (! defined $seen[$n]) {
my ($i, $value) = $seq->next;
if ($value <= $count
&& ! defined $seen[$value]
&& all_odds_0($fibbinary->ith($i))) {
### seen: "$value at i=$i"
$seen[$value] = $i;
}
}
push @got, $seen[$n];
}
$got[0] = 1;
return \@got;
});
sub all_odds_0 {
my ($n) = @_;
while ($n) {
if ($n & 2) { return 0; }
$n >>= 2;
}
return 1;
}
#------------------------------------------------------------------------------
# A083853 - smallest x for which R'(x) = n
# R'(x) counts 1 twice, which is R'(x) = R(x)+R(x-1)
MyOEIS::compare_values
(anum => 'A083853',
func => sub {
my ($count) = @_;
my @got;
my @seen;
my $prev = 0;
my $seq = Math::NumSeq::FibonacciRepresentations->new;
for (my $n = 1; @got < $count; $n++) {
while (! defined $seen[$n]) {
my ($i, $this) = $seq->next;
my $value = $this + $prev;
$prev = $this;
if ($value <= $count && ! defined $seen[$value]) {
### seen: "$value at i=$i"
$seen[$value] = $i;
}
}
push @got, $seen[$n];
}
return \@got;
});
#------------------------------------------------------------------------------
# A013583 - smallest x for which R(x) = n
MyOEIS::compare_values
(anum => 'A013583',
# max_value => 2000000,
func => sub {
my ($count) = @_;
my @got;
my @seen;
my $seq = Math::NumSeq::FibonacciRepresentations->new;
for (my $n = 1; @got < $count; $n++) {
while (! defined $seen[$n]) {
my ($i, $value) = $seq->next;
if ($value <= $count && ! defined $seen[$value]) {
### seen: "$value at i=$i"
$seen[$value] = $i;
}
}
push @got, $seen[$n];
}
$got[0] = 1;
return \@got;
});
#------------------------------------------------------------------------------
exit 0;