Abigail,
I like your logic and agree it should be more efficient with large step sizes, but it doesn't appear to be faster. I've tried the following step sizes on an array of 1000000 elements: 5, 10, 100, 100, etc, 100000, 200000, 300000 & 500000. I bencmarked the results. The output I have included is with the step size of 500000 but is a fair summary of the results I saw:

Benchmark: running Step 1, Step 2, Step 3 for at least 10 CPU seconds.
+..
    Step 1: 10 wallclock secs (10.47 usr +  0.02 sys = 10.49 CPU) @ 18
+5755.48/s (n=1948575)
    Step 2: 11 wallclock secs (10.48 usr +  0.02 sys = 10.50 CPU) @ 18
+7398.10/s (n=1967680)
    Step 3: 10 wallclock secs (10.01 usr +  0.00 sys = 10.01 CPU) @ 31
+5978.92/s (n=3162949)
[download]

Here's the code:

#!/usr/bin/perl -w

use strict;
use Benchmark;

sub step1 {
  my $step = shift;
  @_[map {$_ * $step} 0..($#_ / $step)]; # curious what effect the bac
+kets would have
}

sub step2 {
  my $step = shift;
  @_[map {$_ * $step} 0..$#_ / $step];
}

sub step3 {
  my $step = shift;
  return map { $_[$_] } grep { $_ % $step == 0 } 0..$#_;
}

my @array = (0..1000000);

timethese(-10, {
  'Step 1' => 'step1(500000, @array)',
  'Step 2' => 'step2(500000, @array)',
  'Step 3' => 'step3(500000, @array)'
});
[download]

The only reason I post this is I'm curoius as to why what would appear to be a quicker and more effient piece of code is consistently the slowest (although not by much).

But you are not measuring what you think you are! Once again, the high number of iterations per second Benchmark is reporting should ring many bells and whistles. Do you really think your computer is able to do more than 3 billion modulus operations per second? Because if you believe your Benchmark results, it's grepping through a 1000001 element array 315978.92 times a second. Of course it isn't. You have my @array, which makes that @array is only visible from the file. And not from an eval that's happening in Benchmark.pm (that would defeat all the purposes of my, wouldn't it?), Changing the last lines to:

our @array = (0..1000000);

timethese(-10, {
  'Step 1' => 'step1(500000, @::array)',
  'Step 2' => 'step2(500000, @::array)',
  'Step 3' => 'step3(500000, @::array)'
});
[download]

we get far more sensible results:

Benchmark: running Step 1, Step 2, Step 3 for at least 10 CPU seconds.
+..
  Step 1: 10 wallclock secs (10.17 usr +  0.00 sys = 10.17 CPU) @  5.1
+1/s (n=52)
  Step 2: 10 wallclock secs (10.00 usr +  0.00 sys = 10.00 CPU) @  5.1
+0/s (n=51)
  Step 3: 11 wallclock secs (10.72 usr +  0.00 sys = 10.72 CPU) @  0.4
+7/s (n=5)
[download]

Two things can be learned. First, don't blindly use my. Think whether it's appropriate. Second, always distrust your code if Benchmark returns many iterations per second - especially if you do lots of work during an iteration.

Abigail