#!/usr/bin/perl -w
# Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018 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 => 51;
use lib 't','xt';
use MyTestHelpers;
BEGIN { MyTestHelpers::nowarnings(); }
use MyOEIS;
use Math::PlanePath::DragonCurve;
my $dragon = Math::PlanePath::DragonCurve->new;
sub is_square {
my ($n) = @_;
my $sqrt = int(sqrt($n));
return $n == $sqrt*$sqrt;
}
#------------------------------------------------------------------------------
# Skd num segments in directions to level k
foreach my $elem ([ 'A038503', 0, [1] ],
[ 'A038504', 1, [0] ],
[ 'A038505', 2, [] ],
[ 'A000749', 3, [0] ]) {
my ($anum, $want_dir4, $initial) = @$elem;
MyOEIS::compare_values
(anum => $anum,
max_count => 5,
name => "dir=$want_dir4",
func => sub {
my ($count) = @_;
my @got = @$initial;
require Math::NumSeq::PlanePathDelta;
my $seq = Math::NumSeq::PlanePathDelta->new(planepath_object=>$dragon,
delta_type => 'Dir4');
my $target = 2;
my $total = 0;
while (@got < $count) {
my ($i, $value) = $seq->next;
if ($i == $target) {
push @got, $total;
$target *= 2;
}
$total += ($value == $want_dir4);
}
return \@got;
});
}
#------------------------------------------------------------------------------
# N with dir E,N,W,S
require Math::NumSeq::PlanePathDelta;
foreach my $elem ([ 'A043724', 0, 1], # A043724 doesn't include N=0
[ 'A043725', 1],
[ 'A043726', 2],
[ 'A043727', 3]) {
my ($anum, $want_dir4, $skip) = @$elem;
MyOEIS::compare_values
(anum => $anum,
name => "N of dir4=$want_dir4",
func => sub {
my ($count) = @_;
my @got;
my $seq = Math::NumSeq::PlanePathDelta->new(planepath_object=>$dragon,
delta_type => 'Dir4');
foreach (1 .. $skip||0) { $seq->next; }
while (@got < $count) {
my ($n, $value) = $seq->next;
if ($value == $want_dir4) {
push @got, $n;
}
}
return \@got;
});
}
#------------------------------------------------------------------------------
# A268411 - horizontals 2N direction 0=East, 1=West
MyOEIS::compare_values
(anum => 'A268411',
func => sub {
my ($count) = @_;
my @got;
require Math::NumSeq::PlanePathDelta;
my $seq = Math::NumSeq::PlanePathDelta->new(planepath_object=>$dragon,
delta_type => 'Dir4');
while (@got < $count) {
my ($i, $value) = $seq->next;
push @got, $value/2;
$seq->next; # skip odd N
}
return \@got;
});
#------------------------------------------------------------------------------
# A227741 permutation of the integers,
# each dir many integers in reverse order
MyOEIS::compare_values
(anum => 'A227741',
func => sub {
my ($count) = @_;
my @got;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'LSR');
my $upto = 1;
my $dir = 0;
while (@got < $count) {
my ($i, $value) = $seq->next;
$dir += $value;
push @got, reverse $upto .. $upto+$dir-1;
$upto += $dir;
}
$#got = $count-1;
return \@got;
});
# FORMULA
# A227742 permutation fixed point
#
# middle of each odd dir
# turn +/-1 so dir alternately even,odd
# so per Antti Karttunen A173318(2*(n-1)) + (1/2)*(1 + A005811(2n-1))
#
MyOEIS::compare_values
(anum => 'A227742',
func => sub {
my ($count) = @_;
my @got;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'LSR');
my $upto = 1;
my $dir = 0;
while (@got < $count) {
my ($i, $value) = $seq->next;
$dir += $value;
if ($dir %2) {
push @got, $upto + ($dir-1)/2;
}
$upto += $dir;
}
$#got = $count-1;
return \@got;
});
#------------------------------------------------------------------------------
# A164910 - dragon 1 + cumulative turn +/-1, partial sums of that cumulative
# partial sums A088748
# A001792 = (n+2)*2^(n-1)
# a(4) = 8 = 4*2^1
# a(8) = 20 = 5*2^2
# a(16)= 48 = 6*2^3
# a(32)= 112 = 7*2^4
MyOEIS::compare_values
(anum => 'A164910',
func => sub {
my ($count) = @_;
my @got;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'LSR');
my $cumulative = 1;
my $partial_sum = $cumulative;
while (@got < $count) {
push @got, $partial_sum;
my ($i, $value) = $seq->next;
$cumulative += $value;
$partial_sum += $cumulative;
}
return \@got;
});
# A173318 - dragon cumulative turn +/-1, partial sums of that cumulative
MyOEIS::compare_values
(anum => 'A173318',
func => sub {
my ($count) = @_;
my @got;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'LSR');
my $cumulative = 0;
my $partial_sum = $cumulative;
while (@got < $count) {
push @got, $partial_sum;
my ($i, $value) = $seq->next;
$cumulative += $value;
$partial_sum += $cumulative;
}
return \@got;
});
# A227744 squares among A173318 dragon dir cumulative
MyOEIS::compare_values
(anum => 'A227744',
func => sub {
my ($count) = @_;
my @got;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'LSR');
my $cumulative = 0;
my $partial_sum = $cumulative;
while (@got < $count) {
if (is_square($partial_sum)) {
push @got, $partial_sum;
}
my ($i, $value) = $seq->next;
$cumulative += $value;
$partial_sum += $cumulative;
}
return \@got;
});
# A227743 indexes of squares among A173318 dragon dir cumulative
MyOEIS::compare_values
(anum => 'A227743',
func => sub {
my ($count) = @_;
my @got = (0);
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'LSR');
my $cumulative = 0;
my $partial_sum = $cumulative;
while (@got < $count) {
my ($i, $value) = $seq->next;
$cumulative += $value;
$partial_sum += $cumulative;
if (is_square($partial_sum)) {
push @got, $i;
}
}
return \@got;
});
# A227745 sqrts of squares among A173318 dragon dir cumulative
MyOEIS::compare_values
(anum => 'A227745',
func => sub {
my ($count) = @_;
my @got;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'LSR');
my $cumulative = 0;
my $partial_sum = $cumulative;
while (@got < $count) {
if (is_square($partial_sum)) {
push @got, sqrt($partial_sum);
}
my ($i, $value) = $seq->next;
$cumulative += $value;
$partial_sum += $cumulative;
}
return \@got;
});
#------------------------------------------------------------------------------
# A005811 -- total rotation, count runs of bits in binary
#
MyOEIS::compare_values
(anum => 'A005811',
func => sub {
my ($count) = @_;
my @got;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'LSR');
my $cumulative = 0;
while (@got < $count) {
push @got, $cumulative;
my ($i, $value) = $seq->next;
$cumulative += $value;
}
return \@got;
});
# A136004 total turn + 4
MyOEIS::compare_values
(anum => 'A136004',
func => sub {
my ($count) = @_;
my @got;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'LSR');
my $cumulative = 4;
while (@got < $count) {
push @got, $cumulative;
my ($i, $value) = $seq->next;
$cumulative += $value;
}
return \@got;
});
# A037834 - dragon cumulative turn +/-1
# -1 + sum i=1 to n turn(n)
#
MyOEIS::compare_values
(anum => 'A037834',
func => sub {
my ($count) = @_;
my @got;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'LSR');
my $cumulative = -1; # sum - 1
while (@got < $count) {
my ($i, $value) = $seq->next;
$cumulative += $value;
push @got, $cumulative;
}
return \@got;
});
# A088748 - dragon cumulative turn +/-1
# 1 + sum i=1 to n turn(n)
#
MyOEIS::compare_values
(anum => 'A088748',
func => sub {
my ($count) = @_;
my @got;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'LSR');
my $cumulative = 1; # sum + 1
while (@got < $count) {
push @got, $cumulative;
my ($i, $value) = $seq->next;
$cumulative += $value;
}
return \@got;
});
#------------------------------------------------------------------------------
# A255070 - TurnsR num right turns 1 to N
MyOEIS::compare_values
(anum => 'A255070',
func => sub {
my ($count) = @_;
my @got = (0);
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'Right');
my $total = 0;
while (@got < $count) {
my ($i, $value) = $seq->next;
$total += $value;
push @got, $total;
}
return \@got;
});
# A236840 - 2*TurnsR num right turns 1 to N
MyOEIS::compare_values
(anum => 'A236840',
func => sub {
my ($count) = @_;
my @got = (0);
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'Right');
my $total = 0;
while (@got < $count) {
my ($i, $value) = $seq->next;
$total += $value;
push @got, 2*$total;
}
return \@got;
});
#------------------------------------------------------------------------------
# A090678 - N not start of a turn run, so where turn same as previous
MyOEIS::compare_values
(anum => 'A090678',
func => sub {
my ($count) = @_;
my @got = (1,1);
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'LSR');
(undef, my $prev_value) = $seq->next;
while (@got < $count) {
my ($i, $value) = $seq->next;
push @got, $value == $prev_value ? 1 : 0;
$prev_value = $value;
}
return \@got;
});
#------------------------------------------------------------------------------
# A106836 - N steps between right turns
# with a first term included so start $prev_i=0
MyOEIS::compare_values
(anum => 'A106836',
func => sub {
my ($count) = @_;
my @got;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'Right');
my $prev_i = 0;
while (@got < $count) {
my ($i, $value) = $seq->next;
next unless $value;
if (defined $prev_i) { push @got, $i - $prev_i; }
$prev_i = $i;
}
return \@got;
});
# A088742 - N steps between left turns
# with a first term included so start $prev_i=0
MyOEIS::compare_values
(anum => 'A088742',
func => sub {
my ($count) = @_;
my @got;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'Left');
my $prev_i = 0;
while (@got < $count) {
my ($i, $value) = $seq->next;
next unless $value;
if (defined $prev_i) { push @got, $i - $prev_i; }
$prev_i = $i;
}
return \@got;
});
#------------------------------------------------------------------------------
# Ba2 boundary length of arms=2 around whole of level k
# FIXME: Neither values nor diff are A052537 it seems, what was this mean to be?
# *
# |
# 3 5---* 4 * *---*---*
# | | | | | | |
# o---2 o---* *---* o---*
# len=4 k=2 len=8 k=3 len=14
#
# MyOEIS::compare_values
# (anum => 'A052537',
# max_value => 100,
# func => sub {
# my ($count) = @_;
# my @got;
# my $path = Math::PlanePath::DragonCurve->new (arms => 2);
# my $k = 0;
# my $prev = MyOEIS::path_boundary_length ($path, 2*2**$k + 1);
# for ($k++; @got < $count; $k++) {
# my $len = MyOEIS::path_boundary_length ($path, 2*2**$k + 1);
# my $diff = $len - $prev;
# push @got, $diff;
# $prev = $len;
# }
# return \@got;
# });
#------------------------------------------------------------------------------
# A091067 -- N positions of right turns
MyOEIS::compare_values
(anum => 'A091067',
func => sub {
my ($count) = @_;
my @got;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'Right');
while (@got < $count) {
my ($i, $value) = $seq->next;
if ($value) {
push @got, $i;
}
}
return \@got;
});
# A255068 -- N positions where next turn right
MyOEIS::compare_values
(anum => 'A255068',
name => 'N where next turn right',
func => sub {
my ($count) = @_;
my @got;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'Right');
while (@got < $count) {
my ($i, $value) = $seq->next;
if ($value) {
push @got, $i-1;
}
}
return \@got;
});
# A060833 -- N positions where previous turn right
MyOEIS::compare_values
(anum => 'A060833',
name => 'N where previous turn right',
func => sub {
my ($count) = @_;
my @got = (1); # extra initial 1
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'Right');
while (@got < $count) {
my ($i, $value) = $seq->next;
if ($value) {
push @got, $i+1;
}
}
return \@got;
});
#------------------------------------------------------------------------------
# A091072 -- N positions of left turns
MyOEIS::compare_values
(anum => 'A091072',
func => sub {
my ($count) = @_;
my @got;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'Left');
while (@got < $count) {
my ($i, $value) = $seq->next;
if ($value) {
push @got, $i;
}
}
return \@got;
});
#------------------------------------------------------------------------------
# A099545 -- turn 1=left, 3=right
MyOEIS::compare_values
(anum => 'A099545',
func => sub {
my ($count) = @_;
my @got;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'Left');
while (@got < $count) {
my ($i, $value) = $seq->next;
push @got, $value ? 1 : 3;
}
return \@got;
});
#------------------------------------------------------------------------------
# A003476 Daykin and Tucker alpha[n]
# = RQ squares on right boundary, OFFSET=1 values 1, 2, 3, 5
# = S single points N=0 to N=2^(k-1) inclusive, with initial 1 for k=-1 one point
#
# *
# |
# *---* *---*
#
# k=0 k=1
# singles=2 singles=3
#
#
MyOEIS::compare_values
(anum => 'A003476',
max_value => 10000,
func => sub {
my ($count) = @_;
my @got = (1);
for (my $k = 0; @got < $count; $k++) {
push @got, MyOEIS::path_n_to_singles ($dragon, 2**$k);
}
return \@got;
});
#------------------------------------------------------------------------------
# A121238 - (-1)^(1+n+A088585(n)) is 1=left,-1=right, extra initial 1
# A088585 bisection or partial sums of A088567=non-squashing partitions
# = A088575+1
# A088575 bisection of A088567
# A088567 a(0)=1, a(1)=1;
# for m >= 1, a(2m) = a(2m-1) + a(m) - 1,
# a(2m+1) = a(2m) + 1
# A090678 = A088567 mod 2.
MyOEIS::compare_values
(anum => 'A121238',
func => sub {
my ($count) = @_;
my @got = (1);
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'Left');
while (@got < $count) {
my ($i, $value) = $seq->next;
push @got, $value ? 1 : -1;
}
return \@got;
});
#------------------------------------------------------------------------------
# A166242 - turn cumulative doubling/halving, is 2^(total turn)
MyOEIS::compare_values
(anum => 'A166242',
func => sub {
my ($count) = @_;
my @got = (1);
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'Left');
my $cumulative = 1;
while (@got < $count) {
my ($i, $value) = $seq->next;
if ($value) {
$cumulative *= 2;
} else {
$cumulative /= 2;
}
push @got, $cumulative;
}
return \@got;
});
#------------------------------------------------------------------------------
# A112347 - Kronecker -1/n is 1=left,-1=right, extra initial 0
MyOEIS::compare_values
(anum => 'A112347',
func => sub {
my ($count) = @_;
my @got = (0);
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'Left');
while (@got < $count) {
my ($i, $value) = $seq->next;
push @got, $value ? 1 : -1;
}
return \@got;
});
#------------------------------------------------------------------------------
# A014710 -- turn 2=left, 1=right
MyOEIS::compare_values
(anum => 'A014710',
func => sub {
my ($count) = @_;
my @got;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'Left');
while (@got < $count) {
my ($i, $value) = $seq->next;
push @got, $value+1;
}
return \@got;
});
#------------------------------------------------------------------------------
# A014709 -- turn 1=left, 2=right
MyOEIS::compare_values
(anum => 'A014709',
func => sub {
my ($count) = @_;
my @got;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'Right');
while (@got < $count) {
my ($i, $value) = $seq->next;
push @got, $value+1;
}
return \@got;
});
#------------------------------------------------------------------------------
# A014577 -- turn 1=left, 0=right, starting from 1
#
# cf A059125 is almost but not quite the same, the 8,24,or some such entries
# differ
MyOEIS::compare_values
(anum => 'A014577',
func => sub {
my ($count) = @_;
my @got;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'Left');
while (@got < $count) {
my ($i, $value) = $seq->next;
push @got, $value;
}
return \@got;
});
#------------------------------------------------------------------------------
# A014707 -- turn 0=left, 1=right, starting from 1
MyOEIS::compare_values
(anum => 'A014707',
func => sub {
my ($count) = @_;
my @got;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'Right');
while (@got < $count) {
my ($i, $value) = $seq->next;
push @got, $value;
}
return \@got;
});
#------------------------------------------------------------------------------
# A088431 - dragon turns run lengths
MyOEIS::compare_values
(anum => 'A088431',
func => sub {
my ($count) = @_;
my @got;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'Right');
my ($i, $prev) = $seq->next;
my $run = 1; # count for initial $prev_turn
while (@got < $count) {
my ($i, $value) = $seq->next;
if ($value == $prev) {
$run++;
} else {
push @got, $run;
$run = 1; # count for new $turn value
}
$prev = $value;
}
return \@got;
});
#------------------------------------------------------------------------------
# A007400 - 2 * run lengths, extra initial 0,1
# cf A007400 cont frac 1/2^1 + 1/2^2 + 1/2^4 + 1/2^8 + ... 1/2^(2^n)
# = 0.8164215090218931...
# 2,4,6 values
# a(0)=0,
# a(1)=1,
# a(2)=4,
# a(8n) = a(8n+3) = 2,
# a(8n+4) = a(8n+7) = a(16n+5) = a(16n+14) = 4,
# a(16n+6) = a(16n+13) = 6,
# a(8n+1) = a(4n+1),
# a(8n+2) = a(4n+2)
MyOEIS::compare_values
(anum => 'A007400',
func => sub {
my ($count) = @_;
my @got = (0,1);
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'Right');
my ($i, $prev) = $seq->next;
my $run = 1; # count for initial $prev_turn
while (@got < $count) {
my ($i, $value) = $seq->next;
if ($value == $prev) {
$run++;
} else {
push @got, 2 * $run;
$run = 1; # count for new $turn value
}
$prev = $value;
}
return \@got;
});
#------------------------------------------------------------------------------
# A003460 -- turn 1=left,0=right packed as octal high to low, in 2^n levels
# bit-packing per Gardner, pages 215-217 of reprint in "Mathematical Magic Show"
MyOEIS::compare_values
(anum => 'A003460',
func => sub {
my ($count) = @_;
my @got;
require Math::BigInt;
my $bits = Math::BigInt->new(0);
my $target_n_level = 2;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'Left');
for (my $n = 1; @got < $count; $n++) {
if ($n >= $target_n_level) { # not including n=2^level point itself
my $octal = $bits->as_oct; # new enough Math::BigInt
$octal =~ s/^0+//; # strip leading "0"
push @got, Math::BigInt->new("$octal");
$target_n_level *= 2;
}
my ($i, $value) = $seq->next;
$bits = 2*$bits + $value;
}
return \@got;
});
#------------------------------------------------------------------------------
# A082410 -- complement reversal, is turn 1=left, 0=right
MyOEIS::compare_values
(anum => 'A082410',
func => sub {
my ($count) = @_;
my @got = (0);
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new(planepath_object=>$dragon,
turn_type => 'Left');
while (@got < $count) {
my ($i, $value) = $seq->next;
push @got, $value; # 1=left,0=right
}
return \@got;
});
#------------------------------------------------------------------------------
# A126937 -- points numbered as SquareSpiral, starting N=0
MyOEIS::compare_values
(anum => 'A126937',
func => sub {
my ($count) = @_;
require Math::PlanePath::SquareSpiral;
my $square = Math::PlanePath::SquareSpiral->new (n_start => 0);
my @got;
for (my $n = $dragon->n_start; @got < $count; $n++) {
my ($x, $y) = $dragon->n_to_xy ($n);
my $square_n = $square->xy_to_n ($x, -$y);
push @got, $square_n;
}
return \@got;
});
#------------------------------------------------------------------------------
# A077949 join area increments, ie. first differences
MyOEIS::compare_values
(anum => 'A077949',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got;
my $prev = 0;
for (my $k = 3; @got < $count; $k++) {
my $join_area = $dragon->_UNDOCUMENTED_level_to_enclosed_area_join($k);
push @got, $join_area - $prev;
$prev = $join_area;
}
return \@got;
});
# A003479 join area
MyOEIS::compare_values
(anum => 'A003479',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got;
for (my $k = 3; @got < $count; $k++) {
push @got, $dragon->_UNDOCUMENTED_level_to_enclosed_area_join($k);
}
return \@got;
});
#------------------------------------------------------------------------------
# A003478 enclosed area increment, ie. first differences
MyOEIS::compare_values
(anum => 'A003478',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got;
my $prev_area = 0;
for (my $k = 4; @got < $count; $k++) {
my $area = MyOEIS::path_enclosed_area ($dragon, 2**$k);
push @got, $area - $prev_area;
$prev_area = $area;
}
return \@got;
});
#------------------------------------------------------------------------------
# A003230 enclosed area to N <= 2^k
MyOEIS::compare_values
(anum => 'A003230',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got;
for (my $k = 4; @got < $count; $k++) {
push @got, MyOEIS::path_enclosed_area ($dragon, 2**$k);
}
return \@got;
});
#------------------------------------------------------------------------------
# A164395 single points N=0 to N=2^k-1 inclusive, for k=4 up
# is count binary with no substrings equal to 0001 or 0101
MyOEIS::compare_values
(anum => 'A164395',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got;
for (my $k = 4; @got < $count; $k++) {
push @got, MyOEIS::path_n_to_singles ($dragon, 2**$k - 1);
}
return \@got;
});
#------------------------------------------------------------------------------
# A227036 boundary length N <= 2^k
MyOEIS::compare_values
(anum => 'A227036',
max_value => 10_000,
func => sub {
my ($count) = @_;
my @got;
for (my $k = 0; @got < $count; $k++) {
push @got, MyOEIS::path_boundary_length ($dragon, 2**$k);
}
return \@got;
});
#------------------------------------------------------------------------------
# A038189 -- bit above lowest 1, is 0=left,1=right
MyOEIS::compare_values
(anum => 'A038189',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath => 'DragonCurve',
turn_type => 'Right');
my @got = (0); # extra initial 0
while (@got < $count) {
my ($i,$value) = $seq->next;
push @got, $value;
}
return \@got;
});
# A089013=A038189 but initial extra 1
MyOEIS::compare_values
(anum => 'A089013',
func => sub {
my ($count) = @_;
require Math::NumSeq::PlanePathTurn;
my $seq = Math::NumSeq::PlanePathTurn->new (planepath => 'DragonCurve',
turn_type => 'Right');
my @got = (1); # extra initial 1
while (@got < $count) {
my ($i,$value) = $seq->next;
push @got, $value;
}
return \@got;
});
#------------------------------------------------------------------------------
exit 0;