#!/usr/bin/env perl
# Preferred Numbers: https://perlmonks.org/?node_id=11103336

my $prev = 1;
for my $this ( 2 .. 10 ) {
    # an x% change can fit between $prev and $this
    # x% changes, depending on $this
    # Overlap will start if x% is such that prev * (1+x%) == this * (1-x%)
    #   algebra:
    #       p*(1+x) = t*(1-x)
    #       p + px = t - tx
    #       (p+t)x = t-p
    #       x = (t-p)/(p+t)
    #       x% = 100%*x
    my $xpct = ($this-$prev) / ($this+$prev) * 100;
    printf "linear: %.2f .. %.2f => %.2f%%\n", $prev, $this, $xpct;
} continue {
    $prev = $this;
}

print "\n";

my $prev = 1;
for my $i ( 1 .. 10 ) {
    # now go in 10 logarithmic steps
    $this = $prev * (10**(1/10));
    my $xpct = ($this-$prev) / ($this+$prev) * 100;
    printf "logarithmic: %.2f .. %.2f => %.2f%%\n", $prev, $this, $xpct;
} continue {
    $prev = $this;
}

print "\n";

my $prev = 1;
for my $i ( 1 .. 10 ) {
    # now go in 10 logarithmic steps
    $this = 10**($i/10);
    my $round_p = int($prev*10+0.5)/10;
    my $round_t = int($this*10+0.5)/10;
    my $xpct = ($round_t-$round_p) / ($round_t+$round_p) * 100;
    printf "rounded logarithmic: %.2f .. %.2f => %.2f%%\n", $round_p, $round_t, $xpct;
} continue {
    $prev = $this;
}

__END__
linear: 1.00 .. 2.00 => 33.33%
linear: 2.00 .. 3.00 => 20.00%
linear: 3.00 .. 4.00 => 14.29%
linear: 4.00 .. 5.00 => 11.11%
linear: 5.00 .. 6.00 => 9.09%
linear: 6.00 .. 7.00 => 7.69%
linear: 7.00 .. 8.00 => 6.67%
linear: 8.00 .. 9.00 => 5.88%
linear: 9.00 .. 10.00 => 5.26%

logarithmic: 1.00 .. 1.26 => 11.46%
logarithmic: 1.26 .. 1.58 => 11.46%
logarithmic: 1.58 .. 2.00 => 11.46%
logarithmic: 2.00 .. 2.51 => 11.46%
logarithmic: 2.51 .. 3.16 => 11.46%
logarithmic: 3.16 .. 3.98 => 11.46%
logarithmic: 3.98 .. 5.01 => 11.46%
logarithmic: 5.01 .. 6.31 => 11.46%
logarithmic: 6.31 .. 7.94 => 11.46%
logarithmic: 7.94 .. 10.00 => 11.46%

rounded logarithmic: 1.00 .. 1.30 => 13.04%
rounded logarithmic: 1.30 .. 1.60 => 10.34%
rounded logarithmic: 1.60 .. 2.00 => 11.11%
rounded logarithmic: 2.00 .. 2.50 => 11.11%
rounded logarithmic: 2.50 .. 3.20 => 12.28%
rounded logarithmic: 3.20 .. 4.00 => 11.11%
rounded logarithmic: 4.00 .. 5.00 => 11.11%
rounded logarithmic: 5.00 .. 6.30 => 11.50%
rounded logarithmic: 6.30 .. 7.90 => 11.27%
rounded logarithmic: 7.90 .. 10.00 => 11.73%