I can't make heads or tails of your descriptions and examples. If groups of digits are supposed to be surrounded with underscores (taking in account that N is a digit as well), then why does $correct end in R_345U_299M? I would expect it to end in R_345_U_299_M. Also, the group 69827 doesn't get underscores.

I can make a substitution that matches your descriptions, but that produces quite a different string of $string than $correct is.

my $L = '[A-MO-Za-mo-z]';
my $D = '[0-9N]';

$_ = '423RY75Y69827EC67592C78657N965R345U299M';
s/($L?)($D+)\1/_${1}${2}${1}_/g;         
print $_, "\n";
__END__
_423_R_Y75Y__69827_E_C67592C__78657N965_R_345_U_299_M
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