PreprintCC BY 4.0arXiv
Perturbing the Conway sequence
Abstract
We study the alternating perturbation of Conway's nested recurrence, C(n)=C(C(n−1))+C(n−C(n−1))+(−1)n for n≥ 3, with C(1)=C(2)=1. We prove that the sequence is well defined and satisfies C(n)=ψ−3n+O(n/√(log n)), where ψ>1 is the real root of ψ3=ψ2+1.
Related
BibTeX
@misc{cloitre2026perturbing,
title = {{Perturbing the Conway sequence}},
author = {Benoit Cloitre},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29631},
eprint = {2610.29631},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29631},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Perturbing the Conway sequence
AU - Benoit Cloitre
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29631
UR - https://arxiv.org/abs/2610.29631
AB - We study the alternating perturbation of Conway's nested recurrence, C(n)=C(C(n−1))+C(n−C(n−1))+(−1)^n for n≥ 3, with C(1)=C(2)=1. We prove that the sequence is well defined and satisfies C(n)=ψ^−3n+O(n/√(log n)), where ψ>1 is the real root of ψ^3=ψ^2+1.
ER -