Conway’s Constant

Overview

Conway’s constant, approximately 1.303577, describes the growth rate of the look-and-say sequence. No matter which number you start with, the length of the sequence eventually grows by this same factor each step.

The Look-and-Say Sequence

Conway’s constant is a mathematical constant that arises in the study of the look-and-say sequence, a mathematical sequence discovered by the renowned mathematician John Conway. The look-and-say sequence is generated by repeatedly describing the previous term in the sequence. For example, the sequence starts with the term 1, and each subsequent term is obtained by reading the previous term aloud. The first few terms of the sequence are 1, 11, 21, 1211, 111221, and so on, with each term growing progressively longer.

The Constant (λ)

λ ≈ 1.303577

The constant λ (lambda) is the exponential growth rate of the length of the terms in this sequence as the sequence progresses. The value of λ is approximately 1.303577, and it is an irrational number.

This article was generated from the video transcript of “Conway’s Constant Explained”.
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