Math::N...uctSteps(3)

✨ NAME ✨

Math::NumSeq::DigitProductSteps — multiplicative persistence and digital root 💅

okay so bestie, this is a Perl thing from the User Contributed Perl Documentation, and it's genuinely so cute once you get it, i promise 🫶

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🌸 SYNOPSIS 🌸

use Math::NumSeq::DigitProductSteps;
my $seq = Math::NumSeq::DigitProductSteps->new (values_type => 'count');
my ($i, $value) = $seq->next;

that's it. that's the whole vibe check. make a sequence object, call next on it, get back an index and a value. iconic ✨

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🦋 DESCRIPTION 🦋

so what this thing does is it keeps multiplying the digits of a number together until you're left with a single digit. and the sequence values? they're the count of steps it took to get there. that count has a fancy name: the multiplicative persistence 👑

0,0,..0,0,1,1,..1,1,2,2,2,2,2,1,1,1,1,2,2,2,2,2,3,1,1,1,2,...
starting i=0

like, take i=39. it goes 3*9=27 → 2*7=14 → 1*4=4 to reach a single digit, so the value is 3 iterations. three whole steps, main character energy 💅

then if you pass values_type => 'root' you get the final digit you landed on instead, which is called the multiplicative digital root 🌈

values_type => 'root'
0,1,2,...,9,0,1,...,9,0,2,4,6,8,0,2,4,6,8,0,3,6,9,2,5,8,...

and here's the tea:

• i=0 through i=9 are already single digits, so their count is 0 and their root is just the value itself. no work needed, slay 💖
• i=10 to i=19 all take just a single iteration to reach a single digit.
• i=25 is the first one that needs 2 iterations. not me being dramatic about i=25 but it IS the first ok 😭

more lore: any i with a 0 digit takes just one iteration to get to root 0. and any i like 119111 — all 1s except for at most a single non-1 — also takes just one iteration. this includes the repunits 111..11 ✨ (yes bestie, repunits are a real word and they're kinda iconic)

🌟 Radix 🌟

there's an optional radix parameter that picks a base other than decimal, if you're feeling spicy 🌶️

binary radix=>2 is not very interesting tho, sorry — the digit product is always either 0 or 1. i>=2 always takes just 1 iteration and has root 0, except for i=2^k-1 which is all 1s and has root 1. that's the whole binary situation. lowkey uneventful but we respect it 🫡

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💖 FUNCTIONS 💖

peep "FUNCTIONS" in Math::NumSeq for the behaviour that's common to all sequence classes, bestie — this page is just the special stuff 🎀

• $seq = Math::NumSeq::DigitProductSteps->new ()
• $seq = Math::NumSeq::DigitProductSteps->new (values_type => $str, radix => $integer)

create and return a brand new sequence object. new object, new era, periodt ✨

🎀 Random Access 🎀

• $value = $seq->ith($i) — return the sequence value, either the count or the final root value, whichever you selected. your pick, your power 💅
• $bool = $seq->pred($value) — return true if $value occurs in the sequence. for the count of steps this means any integer "$value >= 0", or for a root, any digit "0 <= $value < radix". simple as that 🫶

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👀 SEE ALSO 👀

• Math::NumSeq
• Math::NumSeq::DigitProduct

go read those too, i'm obsessed with a well-organized module family 💜

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🌐 HOME PAGE 🌐

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

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📜 LICENSE 📜

Copyright 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/>.

bestie that warranty disclaimer is doing the MOST and honestly? respect. no cap, read your licenses 💀

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and that's the whole page!! this was Math::N...uctSteps(3) from perl v5.42.0, dated 2025-07-25 — mwah, ty for reading, go multiply some digits, ily 🫶💖✨