Transforming your "lookup" array into a set of hash keys is one widely used way of doing this.

#! /usr/bin/perl
use strict ;
use warnings ;

my @first  = qw( 1 3 5 7 9 11 13 15 17 19 21 23 ) ;
my @second = qw( 1   5   9    13    17    21    ) ;

## Turn the second array into hash keys.
my %hash = map { $_ => 1 } @second ;

my $rand_el = $first[ int rand @first ] ;
print $rand_el . (
                     $hash{$rand_el}
                   ? ' is '
                   : ' is not '
                 ) . 'in the second array.' . "\n" ;

exit ;
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DamnDirtyApe

Those who know that they are profound strive for clarity. Those who
would like to seem profound to the crowd strive for obscurity.
            --Friedrich Nietzsche