Seeing that you're looking for other ways to do it, I offer this, which solves the general case of validating any sequence where the value of N_n depends only on N_n-1:

# first the sequences to test
my @sequences = (
    [qw(1 2 3 4 5)],    # start at 1, inc by 1
    [qw(1 3 5 7 9)],    # start at 1, inc by 2
    [qw(0 1 0 1 0)],    # start at 0, alternate 0/1
    [qw(2 1 0 -1 -2)]   # start at 2, dec by 1
);

# the functions to test them against - each one should
# match just one of the sequences above
my @functions =(
    { text => 'start at 1, increment by 1',
      start => 1,
      function => sub { $_[0] + 1 }
    },
    { text => 'start at 1, increment by 2',
      start => 1,
      function => sub { $_[0] + 2 }
    },
    { text => 'start at 0, alternate 0/1',
      start => 0,
      function => sub { ($_[0] == 0) ? 1 : 0 }
    },
    { text => 'start at 2, decrement by 1',
      start => 2,
      function => sub { $_[0] - 1 }
    }
);

foreach my $function (@functions) {
    print $function->{text}."\n";
    foreach my $sequence (@sequences) {
        print '  ';
        print 'not ' unless(
            checksequence(
                @{$sequence},
                $function->{start},
                $function->{function}
            )
        );
        print 'ok ['.join(', ', @{$sequence})."]\n";
    }
}

# takes a sequence, the desired start value, and the
# function to generate the next correct value
sub checksequence {
    # the sequence is the most important parameter, so
    # i pass it first.
    my($f, $z, @seq) = reverse(@_);
    @seq = reverse(@seq);

    # check that the first value is correct
    return 0 unless(shift(@seq) == $z);

    # now see if any subsequent values are wrong and
    # if they are, return immediately
    foreach my $value (@seq) {
        return 0 unless(($z = $f->($z)) == $value);
    }
    1;
}
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Of course, with some devious and evil trickery the function you pass in to checksequence() could maintain some state information, so it could check more complicated sequences where a value depends on more than just its immediate predecessor.