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#!/usr/bin/perl -w
# Copyright 2011, 2012 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 5.006;
use strict;
use warnings;
use List::Util qw(max);
use Devel::Comments;
{
require Math::PlanePath::DiamondArms;
my @max;
my $path = Math::PlanePath::DiamondArms->new;
foreach my $n (2 .. 10000) {
my ($x,$y) = $path->n_to_xy($n);
$x = abs($x);
$y = abs($y);
my $d = abs($x)+abs($y);
$max[$d] ||= 0;
$max[$d] = max($max[$d], $n);
}
### @max
exit 0;
}
{
require Math::PlanePath::HexArms;
my @max;
my $path = Math::PlanePath::HexArms->new;
foreach my $n (2 .. 10000) {
my ($x,$y) = $path->n_to_xy($n);
$x = abs($x);
$y = abs($y);
my $d = ($y >= $x
? $y # middle
: ($x + $y)/2); # end
$max[$d] ||= 0;
$max[$d] = max($max[$d], $n);
}
### @max
exit 0;
}
{
# cf A094268 smallest of N consecutive abundants
# 5775 pair (3,4 mod 6)
# 171078830 triplet (2,3,4 mod 6)
# 141363708067871564084949719820472453374 first run of 4 consecutive
#
# cf A047802 first abundant not using the first N primes
#
my $limit = 33426748355;
my $min = $limit;
my $divsum = 1;
for (my $p5 = 0; ; $p5++) {
my $value = 5**$p5;
last if $value > $limit;
my $divsum = (5**($p5+1) - 1) / 4;
for (my $p7 = 0; ; $p7++) {
my $value = $value * 7**$p7;
last if $value > $limit;
my $divsum = $divsum * (7**($p7+1) - 1) / 6;
for (my $p11 = 0; ; $p11++) {
my $value = $value * 11**$p11;
last if $value > $limit;
my $divsum = $divsum * (11**($p11+1) - 1) / 10;
for (my $p13 = 0; ; $p13++) {
my $value = $value * 13**$p13;
last if $value > $limit;
my $divsum = $divsum * (13**($p13+1) - 1) / 12;
for (my $p17 = 0; ; $p17++) {
my $value = $value * 17**$p17;
last if $value > $limit;
my $divsum = $divsum * (17**($p17+1) - 1) / 16;
for (my $p19 = 0; ; $p19++) {
my $value = $value * 19**$p19;
last if $value > $limit;
my $divsum = $divsum * (19**($p19+1) - 1) / 18;
for (my $p23 = 0; ; $p23++) {
my $value = $value * 23**$p23;
last if $value > $limit;
my $divsum = $divsum * (23**($p23+1) - 1) / 22;
for (my $p29 = 0; ; $p29++) {
my $value = $value * 29**$p29;
last if $value > $limit;
my $divsum = $divsum * (29**($p29+1) - 1) / 28;
for (my $p31 = 0; ; $p31++) {
my $value = $value * 31**$p31;
last if $value > $limit;
my $divsum = $divsum * (31**($p31+1) - 1) / 30;
if ($divsum > 2*$value) {
print "value $value divsum $divsum\n";
print "$p5 $p7 $p11 $p13 $p17 $p19 $p23 $p29 $p31\n";
if ($value < $min) {
print " smaller\n";
$min = $value;
}
print "\n";
last;
}
}
}
}
}
}
}
}
}
}
exit 0;
}
{
# 7^k divisors 1,...,7^k
# sum = (7^(k+1)-1)/6
# sum/7^k = (7 - 1/7^k) / 6
# -> 7/6
# single 1,7
# sum = 7+1 = 8
# sum/7 = 8/7
#
use Math::BigInt;
require Math::Prime::XS;
my @primes = Math::Prime::XS::sieve_primes(10000);
my $prod = 1;
my $value = 1;
# for (my $i = 7; $i < 1000; $i += 6) {
foreach my $i (@primes) {
if (($i % 6) != 1
&& ($i % 6) != 5
) {
next;
}
# my $f = $i/($i-1);
my $f = ($i+1)/$i;
$prod *= $f;
$value *= $i;
print "$i $prod\n";
if ($prod > 2) {
last;
}
}
print "value $value\n";
exit 0;
}
{
# 7^k divisors 1,...,7^k = (7^(k+1)-1)/6
use Math::BigInt;
foreach my $i (1 .. 200) {
foreach my $j (0 .. 10) {
foreach my $k (0 .. 10) {
my $n = Math::BigInt->new(7)**$i
* Math::BigInt->new(13)**$j
* Math::BigInt->new(19)**$k;
my $sd = (Math::BigInt->new(7)**($i+1) - 1) / 6
* (Math::BigInt->new(13)**($j+1) - 1) / 12
* (Math::BigInt->new(19)**($k+1) - 1) / 18;
if ($sd >= 2*$n) {
print "$i, $j $n $sd\n";
}
}
}
}
exit 0;
}
{
require Math::NumSeq::Abundant;
my $seq = Math::NumSeq::Abundant->new (hi => 5_000_000);
my ($max_i, $max_value);
while (my ($i, $value) = $seq->next) {
# my $m = ($value % 6);
# if ($m == 1 || $m == 5) {
# print "$i $value is $m mod 6\n";
# }
if ($value % 2) {
print "$i $value odd\n";
}
($max_i, $max_value) = ($i, $value);
}
print "to $max_i $max_value\n";
exit 0;
}
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