Depends on the system: if you've got a 32-bit IV (perl -V:ivsize or perl -MConfig -le 'print $Config{ivsize}' will show 4 bytes for 32-bit, 8 bytes for 64-bit), then even that won't work, because it will overrun the 32-bit integer at 1<<32 - 1. And even with 64 bits, it will stop working above 64:

require v5.16;
use Test::More qw(no_plan);

for(51..66)
 {my $s = sprintf("%b", 1 << $_ -1);
  is length($s), $_, "1 << $_ -1";
 }
__END__
ok 1 - (1 << 51) -1
ok 2 - (1 << 52) -1
ok 3 - (1 << 53) -1
ok 4 - (1 << 54) -1
ok 5 - (1 << 55) -1
ok 6 - (1 << 56) -1
ok 7 - (1 << 57) -1
ok 8 - (1 << 58) -1
ok 9 - (1 << 59) -1
ok 10 - (1 << 60) -1
ok 11 - (1 << 61) -1
ok 12 - (1 << 62) -1
ok 13 - (1 << 63) -1
ok 14 - (1 << 64) -1
not ok 15 - (1 << 65) -1
#   Failed test '(1 << 65) -1'
#   at - line 6.
#          got: '64'
#     expected: '65'
not ok 16 - (1 << 66) -1
#   Failed test '(1 << 66) -1'
#   at - line 6.
#          got: '64'
#     expected: '66'
1..16
# Looks like you failed 2 tests of 16.
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So, philiprbrenan, "is this something to worry about?" depends on what you want to do. It's doing exactly what's expected for a double-float NV. And my example code does what's expected for a 64-bit integer. But as to whether that's behavior to worry about depends on what you're trying to do with your 2**$_n-1.