Math::N...ntSteps(3)

💖 Math::NumSeq::TotientSteps 💖

okay bestie, so this is a page from the User Contributed Perl Documentation — that's the manual name, it lives in the perl man pages, and honestly? it's kind of iconic. 🎀

The module itself is Math::NumSeq::TotientSteps — count of repeated totients to reach 1. yes. that. 🦋

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✨ NAME ✨

Math::NumSeq::TotientSteps — count of repeated totients to reach 1. periodt. 💅

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🌸 SYNOPSIS 🌸

like, the bare minimum to get going:

use Math::NumSeq::TotientSteps;
my $seq = Math::NumSeq::TotientSteps->new;
my ($i, $value) = $seq->next;

that's it. that's the whole vibe. 💜

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🌈 DESCRIPTION 🌈

so the question this answers is: how many times do you gotta hit a number with the totient function before you land on 1? 🧚 and it starts counting from i=1, giving you this little sequence:

0, 1, 2, 2, 3, 2, 3, 3, 3, 3, 4, 3, 4, ...

and like, a concrete example so it clicks — i=5 goes

5 -> 4 -> 2 -> 1

so value=3 steps. no cap. 🔥

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👑 FUNCTIONS 👑

bestie, first the housekeeping: see "FUNCTIONS" in Math::NumSeq for the behaviour that's common to all the sequence classes. shared lore, iykyk. 🫶

• $seq = Math::NumSeq::TotientSteps->new () — creates and returns you a brand new sequence object. main character energy from the jump. ✨

🔮 Random Access 🔮

• $value = $seq->ith($i) — hands you back the count of totient(i) steps it takes to get all the way down to 1. 💫
• $value = $seq->pred($value) — returns true if $value shows up in the sequence, which basically just means a count where "$value >= 0". simple as that. 💖

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🦋 SEE ALSO 🦋

go read these too, they're the friend group:

• Math::NumSeq
• Math::NumSeq::Totient
• Math::NumSeq::TotientStepsSum
• Math::NumSeq::DedekindPsiSteps

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🏠 HOME PAGE 🏠

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

the house. go visit. 🌸

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📜 LICENSE 📜

Copyright 2011, 2012, 2013, 2014, 2016, 2019, 2020, 2021 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/.

okay real talk for one sec — that "WITHOUT ANY WARRANTY" part is not a joke, it's literally in there, so don't come for anyone if it breaks. 💀

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and that's the whole page bestie, you ate it. 💅✨ this was Math::N...ntSteps(3) (yes the man page title really do be abbreviating like that, it's giving truncated 💀), shipping out of perl v5.42.0 and dated 2025-07-25. slay, goodbye, go compute some totients. 🎀🦋💖