prog.pl

#!/usr/bin/perl

# Values of n such that 5^n ends in n, or expomorphic numbers relative to "base" 5.
# https://oeis.org/A306570

use 5.014;
use ntheory qw(:all);

#foreach my $n(408203125..8408203125) {
    #my $n = $k * 5**14;
   # my $n = int(rand(8408203125-408203125)) + 408203125;
 #   if (powmod(5, $n, 10**length($n)) eq $n) {
  #      say "Found: $n";
   # }
#}


use Math::AnyNum qw(:overload);

my $t = 5;

for (1..20) {

    foreach my $k(1..1e6) {

        my $n = Math::AnyNum->new("$k$t");
        if (powmod(5, $n, 10**length($n)) == $n) {
            say $n;
            $t = $n;
            last;
        }
    }

}


__END__

8408203125, 18408203125, 618408203125, 2618408203125, 52618408203125, 152618408203125, 3152618408203125


      8408203125
     18408203125
    618408203125
   2618408203125
  52618408203125
 152618408203125
3152618408203125

25
125
3125
203125
8203125
408203125
8408203125
18408203125
618408203125
2618408203125
52618408203125
152618408203125
3152618408203125
93152618408203125
493152618408203125
7493152618408203125
17493152618408203125
117493152618408203125
7117493152618408203125
87117493152618408203125