Math::N...mModulo(3)

💖 Math::N...mModulo(3) 💖

okay bestie, so this lil page comes from the User Contributed Perl Documentation manual (the title up top is a lil mangled as Math::N...mModulo(3), it's just giving truncated filename energy, we move 💅). Sit down, grab a boba, and let's talk digit sums.

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✨ NAME ✨

Math::NumSeq::DigitSumModulo — digit sum taken modulo a given modulus. periodt.

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🌸 SYNOPSIS 🌸

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

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🦋 DESCRIPTION 🦋

So basically: take each i, add up all its digits, and then take that sum modulo the radix or modulo a modulus you pick. That's the whole vibe.

Like fr fr, at i=123 with modulus 5 the value is 1+2+3=6, mod 5 = 1. Math is mathing. 💖

Modulus 0, which is the default, means modulo the radix. no cap, that's just what it does.

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🎀 Thue-Morse Sequence 🎀

Okay this part is iconic. 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. Not me learning that "evil numbers" is a real technical term. 🙈

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👑 FUNCTIONS 👑

See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes. (Like, all the shared lore. iykyk.)

• $seq = Math::NumSeq::DigitSumModulo->new (radix => $r, modulus => $d) — Create and return a new sequence object. main character constructor behavior, honestly.

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🔥 Random Access 🔥

• $value = $seq->ith($i) — Return the sum of the digits in $i written in "radix", modulo the "modulus". yes bestie, random access, we're not looping from the start like a peasant.
• $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). ✨

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🌈 SEE ALSO 🌈

• Math::NumSeq
• Math::NumSeq::DigitSum
• Math::NumSeq::MephistoWaltz

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🧚 HOME PAGE 🧚

<http://user42.tuxfamily.org/math-numseq/index.html>

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💜 LICENSE 💜

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 <http://www.gnu.org/licenses/>.

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and that's the whole page, babe 🫶 this was perl v5.42.0, dated 2025-07-25, filed under Math::N...mModulo(3). slay, go compute some digit sums 💅✨🍓