Math::NumSeq::DigitSumModulo -- digit sum taken modulo a given modulus


 use Math::NumSeq::DigitSumModulo;
 my $seq = Math::NumSeq::DigitSumModulo->new (radix => 10,
                                              modulus => 9);
 my ($i, $value) = $seq->next;


The sum of digits in each i, taken modulo the radix or a given modulus. For example at i=123 with modulus 5 the value is 1+2+3=6, mod 5 = 1.

Modulus 0, which is the default, means modulo the radix.

Thue-Morse Sequence

For radix=>2, modulus=>2 this is the Thue-Morse "parity" sequence, being 1 if i has an odd number of 1 bits or 0 if an even number of 1 bits. Numbers where it's 1 are sometimes called "odious" numbers and where it's 0 called "evil" numbers.


See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.

$seq = Math::NumSeq::DigitSumModulo->new (radix => $r, modulus => $d)

Create and return a new sequence object.

Random Access

$value = $seq->ith($i)

Return the sum of the digits in $i written in radix, modulo the modulus.

$bool = $seq->pred($value)

Return true if $value might occur as value in the sequence, which means simply $value = 0> and $value <= modulus (the given modulus or the radix if modulus=0).


Math::NumSeq, Math::NumSeq::DigitSum, Math::NumSeq::MephistoWaltz



Copyright 2011, 2012, 2013, 2014, 2016, 2019, 2020 Kevin Ryde

Math-NumSeq is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.

Math-NumSeq is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with Math-NumSeq. If not, see <>.