Math::N...erSteps(3)

💖 NAME 💖

Math::NumSeq::JugglerSteps — bestie, this is the number of steps in the juggler sqrt sequence. Yes that's the whole job. She counts. She's an icon. 👑

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✨ SYNOPSIS ✨

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

okay so literally three lines and you're in. slay. 💅

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🦋 DESCRIPTION 🦋

This is the number of steps it takes to reach 1 by the Juggler sqrt sequence, and the rule is giving ✨two moods✨:

n ->  /  floor(n^(1/2))      if n even
      \  floor(n^(3/2))      if n odd

So: if n is even you take sqrt, and if n is odd you take sqrt(n^3), and either way you round downwards. no exceptions. periodt.

For example, i=17 goes 17 -> sqrt(17^3)=70 -> sqrt(70)=8 -> sqrt(8)=2 -> sqrt(2)=1, for a count of 4 steps. the way that just works out?? obsessed. 😭

0, 1, 6, 2, 5, 2, 4, 2, 7, 7, 4, 7, 4, 7, 6, 3, 4, 3, 9, 3, ...
starting i=1

🫶 heads up bestie: the intermediate values in the calculation can become quite large and Math::BigInt is used if necessary. There's some secret experimental caching in a temporary file, for a small speedup. it's giving mysterious. don't ask. 🤫

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🎀 FUNCTIONS 🎀

See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes. (that's the family, they all share these vibes.)

• $seq = Math::NumSeq::JugglerSteps->new ()
• $seq = Math::NumSeq::JugglerSteps->new (step_type => 'both', juggler_type => '1/2-3/2')

Create and return a new sequence object. ur main character moment. 🌟

The optional step_type parameter (a string) selects between:

• "up" — upward steps sqrt(n^3)
• "down" — downward steps sqrt(n)
• "both" — both up and down, which is the default

The optional juggler_type parameter (a string) selects among variations on the powering:

                  n even        n odd
"1/2-3/2"    sqrt(n)   and sqrt(n^3)
"2/3-3/2"    cbrt(n^2) and sqrt(n^3)
"3/4-4/3"    n^(3/4)   and n^(4/3)

🌸 Random Access 🌸

• $value = $seq->ith($i) — Return the number of steps to take $i down to 1. it's giving direct access, no queueing. ⭐
• $bool = $seq->pred($value) — Return true if $value occurs as a step count. This is simply "$value >= 0". that's it. that's the whole check. lowkey elegant. 💜

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🌈 SEE ALSO 🌈

• Math::NumSeq
• Math::NumSeq::CollatzSteps
• Math::NumSeq::ReverseAddSteps

(the whole squad, go say hi 🫶)

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🧚 HOME PAGE 🧚

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

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👑 LICENSE 👑

Copyright 2010, 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. (fr fr, no promises, read the fine print 💀)

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 bestie 💖 this lil number-crunching legend ships as part of perl v5.42.0, dated 2025-07-25. go forth and juggle some steps ✨🎀