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tall_man,
The only thing that is recursive is merge() which could also be iterative. I believe it does what you want.
```#!/usr/bin/perl
use strict;
use warnings;

use constant HEAD =>  0;
use constant TAIL => -1;

# Usage my \$next = genHam( take => #, list => [<factors>] );
# If take is not specified, it assumes infinity

my \$next = genHam( take => 23, list => [2, 3, 5] );
while ( my \$n = \$next->() ) {
print "\$n\n";
}

sub genHam {
die "Incorrect number of arguments" if @_ % 2;
my %arg = @_;
return () if ! exists \$arg{list} || ref \$arg{list} ne 'ARRAY';

\$arg{take} ||= -1;
my \$n = 0;

my (@pool, @stream);
push @stream, [] for 0 .. \$#{ \$arg{list} };
\$stream[TAIL] = [ \$arg{list}->[TAIL] ];

return sub {
return () if ! \$arg{take}--;

# Return obligatory 1
return ++\$n if ! \$n;

# No need to generate as we already have some in the pool
return shift @pool if @pool;

# Increase highest factor
\$stream[TAIL] = [ \$arg{list}->[TAIL] * \$n ];
++\$n;

# Generate streams of multiples >= highest factor
for my \$i ( 0 .. \$#stream - 1 ) {
# Start with empty stream
\$stream[ \$i ] = [];

my \$multiple = \$arg{list}->[ \$i ];

# Determine what multiple each factor should start at
my \$start = \$n > 2 ? (\$arg{list}->[TAIL] * (\$n - 2)) / \$mu
+ltiple + 1 : 1;

# Add multiples to the stream less than or equal to the hi
+ghest factor
for ( \$start .. \$stream[TAIL]->[HEAD] / \$multiple ) {
push @{ \$stream[ \$i ] }, \$multiple * \$_;
}
}

# Merge streams into new pool
@pool = @{ \$stream[HEAD] };
for ( 1 .. \$#stream ) {
@pool = merge(\@pool, \$stream[ \$_ ]);
}

# Return first member of pool
return shift @pool;
}
}

sub merge {
my (\$s1, \$s2) = @_;
return @\$s2 if ! @\$s1;
return @\$s1 if ! @\$s2;

return shift @\$s1, merge( @_ ) if \$s1->[HEAD] < \$s2->[HEAD];
return shift @\$s2, merge( @_ ) if \$s1->[HEAD] > \$s2->[HEAD];

shift @\$s1;
return shift @\$s2, merge( @_ );
}
[download]```

Cheers - L~R

Update: This is wrong. I was so focused on lazy evaluation that I misunderstood "how do you generate the series of numbers composed of a given list of prime factors, where each can be used an unlimited number of times?" To me, that meant any positive multiple of any factor was valid.

In reply to Re: Hamming Sequences and Lazy Lists by Limbic~Region
in thread Hamming Sequences and Lazy Lists by tall_man

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