# A Chaotic Cousin Of Conway's Recursive Sequence

Source: [A Chaotic Cousin Of Conway's Recursive Sequence](<https://www.sota2.com/research/paper/68fa1ea17a2b558e29323986>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-23T15:28:16.665Z

Authors: K. Pinn

Published: 1998-08-04T08:55:14.000Z

## Abstract

I study the recurrence D(n)= D(D(n-1))+D(n-1-D(n-2)), D(1)=D(2)=1. Its definition has some similarity to that of Conway's sequence defined through a(n)= a(a(n-1))+a(n-a(n-1)), a(1)=a(2)=1. However, in contradistinction to the completely regular and predictable behaviour of a(n), the D-numbers exhibit chaotic patterns. In its statistical properties, the D-sequence shows striking similarities with Hofstadter's Q(n)-sequence, defined through Q(n)= Q(n-Q(n-1))+Q(n-Q(n-2)), Q(1)=Q(2)=1. Compared to the Hofstadter sequence, the D-recurrence shows higher structural order. It is organized in well-defined \`\`generations'', separated by smooth and predictable regions. The article is complemented by a study of two further recurrence relations with definitions similar to those of the Q-numbers. There is some evidence that the different sequences studied share a universality class. Could it be that there are some real life processes modelled by these recurrences? I OFFER A CASH PRIZE OF $100 TO THE FIRST PROVIDING A PROOF OF SOME CONJECTURES ABOUT D(n) FORMULATED IN THIS ARTICLE.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9808031>)

[PDF](<https://arxiv.org/pdf/cond-mat/9808031.pdf>)