Visual Patterns for Identifying Taxicab Numbers
收藏Zenodo2025-11-09 更新2026-05-26 收录
下载链接：
https://zenodo.org/doi/10.5281/zenodo.17564161
下载链接
链接失效反馈官方服务：
资源简介：
This preprint introduces six visual digit patterns that identify all six known taxicab numbers (Ta(2) through Ta(6)) without computing cubes. Each pattern — 9/8 Cycle, 8↔10 Loop, 2:3→13, 4+Collapse, 3-Minus-Position, and Hidden 1 + 1-2-3 Braid — matches exactly one known taxicab number and fails on 1,000 randomly generated integers.
Validation shows 100% specificity: all known Ta(k) are detected, and zero false positives occur in random samples. The patterns serve as a rapid, cube-free pre-filter for taxicab number candidates.
This work invites verification, generalization to higher Ta(k), and exploration of whether digit structure reflects underlying algebraic constraints. Open to collaboration and formal analysis.
Keywords: taxicab numbers, digit patterns, number theory, pattern recognition, Ta(k)
提供机构：
Zenodo创建时间：
2025-11-09
