i don't see any way to do it besides eating letters from the back, then starting over from the front.

here is one way, though index() would surely be faster than m// here.

my $sequence = "GAATGTTTTAGCAATCTCTTTCTGTCATGAATCCATGGCAGTGACCATACTAAT
+GGTGACTGCCATTGATGGAGGGAGACACA";
my $find = "CTGGATAAGAATGTTTTAGCAATCTCTT";

my $found;

MATCH: {
    my $tail = $find;
    while ( length($tail) > 2 and not $found ) {
        ($found) = $sequence =~ /($tail)/  # find match
            or substr( $tail, 0, 1, '');   # or eat first letter

    }
    last MATCH if $found;

    my $head = $find;
    ## can chop first since exact match already failed
    while ( chop $head and length($head) > 2 and not $found ) {
        ($found) = $sequence =~ /($head)/;
    }
}

print "found? $found\n";
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updated: to provide better(?) var names