#!/usr/bin/perl -w

#

# Caluclate Buenos Aires constant - https://youtu.be/_gCKX6VMvmU

# Alternate sum of infinite series method

# (C)Nov 26 2020 Pegasus Epsilon - Educational Purposes Only

#

# premise:

#

# A C A*D + B*C

# --- + --- == -----------

# B D B*D

#

# X = product of previous denominators

#

# (P(n - 1) - 1) (P(n) - 1)

# ---------------- + --------------

# X X * P(n - 1)

#

# N = previous numerator

#

# newN = N*X*P(n-1) + X*(P(n) - 1)

# newX = X*X*P(n-1)

#

# num = oldnum * newden + newnum * oldden

# den *= newden

use strict;

use Math::BigFloat;

use v5.10;

@_ = map { chomp; $_ } <DATA>; # read saved data

close DATA;

my ($op,$obn,$obd) = ($_[$#_] =~ /(.*),(.*),(.*)/); # split the last entry

@_ = map { /([^,]*)/ } @_; # discard the constant convergence log

open my $data, '>>', $0;

sub divide { Math::BigFloat->new(shift)->fdiv(shift, 2 * length shift) }

sub product { my $prod = 1; $prod *= $_ for @_; $prod }

say "resuming from $op";

say "Buenos Aires constant: $obn / $obd = ".divide($obn, $obd, $obn);

my $nbd = $obd;

for (my $np = $op; ; $np++) {

my $sqrt = sqrt($np);

unless ($sqrt == int($sqrt)) {

foreach my $d (@_) {

last if 0 == $np % $d;

next if $d < $sqrt;

say "$np is prime";

$nbd *= $op;

say "add ($np - 1) / $nbd = ".(($np - 1) / $nbd);

my $nbn = $obn * $obd * $op + $obd * ($np - 1);

say "obd: $obd, nbd: $nbd";

say "obn: $obn, nbn: $nbn";

say "Buenos Aires constant: ".divide($nbn, $nbd, $nbn);

push @_, $np;

($op, $obn, $obd) = ($np, $nbn, $nbd);

last;

}

}

}

#2: ... + 2 - 1 / 1 = 1/1 `-=> 1

#3: ... + 3 - 1 / 2 = 2/ 2 = 1/1 `-=> 2

#5: ... + 5 - 1 / 6 = 4/ 6 = 2/3 `-=> 2.666

#7: ... + 7 - 1 / 30 = 6/30 = 1/5 `-=> 2.866

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