Math::N...Numbers(3)

💖 NAME 💖

Math::NumSeq::WoodallNumbers — bestie, it's literally the Woodall numbers, aka i*2^i-1, and yes she's iconic 💅

This page lives in the User Contributed Perl Documentation section, section 3 of the manual, and we're about to have the cutest little math moment together 🧚

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✨ SYNOPSIS ✨

okay so first things first, you load her up and she starts feeding you numbers:

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

that's it. that's the whole vibe. 🦋

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🌸 DESCRIPTION 🌸

The Woodall numbers are i*2^i-1, and the sequence starts from i=1, no cap:

1, 7, 23, 63, 159, 383, 895, 2047, 4607, 10239, ...

look at them go 😭 she's serving numbers fr fr.

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👑 FUNCTIONS 👑

see "FUNCTIONS" in Math::NumSeq for the behaviour common to all sequence classes — that's the group chat everybody's in 💜

• "$seq = Math::NumSeq::WoodallNumbers->new ()" — creates and returns a brand new sequence object. new bestie, who dis 🎀

🦋 Iterating 🦋

• "$seq->seek_to_i($i)" — moves the current sequence position to $i. the very next call to next() will hand you back $i and its corresponding value. it's giving teleportation ✨

💅 Random Access 💅

• "$value = $seq->ith($i)" — returns "$i * 2**$i - 1". that's the formula, she said what she said.
• "$bool = $seq->pred($value)" — returns true if $value is a Woodall number, ie. if it's equal to i*2^i-1 for some i. vibe check: passed or not 🌈
• "$i = $seq->value_to_i_floor($value)" — returns the index i of $value, or the index of the next Woodall number below $value. floor queen 👑
• "$i = $seq->value_to_i_estimate($value)" — returns an estimate of the i corresponding to $value. not exact, just a guess, and honestly same 😭

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🧮 FORMULAS 🧮

⭐ Value to i Estimate ⭐

An easy over-estimate is l=log2(value), which reverses value=2^l. It can be reduced by the bit length of that l as i=l-log2(l) to get closer. math ate that fr fr 🔥

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🫶 SEE ALSO 🫶

• Math::NumSeq
• Math::NumSeq::CullenNumbers
• Math::NumSeq::ProthNumbers

the whole friend group 💖

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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/>.

not the "no warranty" part bestie, that one's serious — if it breaks, it breaks, and nobody's coming to fix it for you 💀

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and that's the whole page, periodt 🎀 this was perl v5.42.0, dated 2025-07-25, and she's still out here being Math::N...Numbers(3) like the icon she is 💅✨ stay slaying, bestie 💖