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On min-base palindromic representations of powers of 2

Donald L. Kreher, Douglas R. Stinson

Abstract

A positive integer $N$ is \emph{palindromic in the base $b$} when $N = \sum_{i=0}^{k} c_i b^i$, $c_k\neq 0$,and $c_i=c_{k-i},\; i=0,1,2,...,k$, Focusing on powers of 2, we investigate the smallest base $b$ when $N=2^n$ is palindromic in the base $b$.

On min-base palindromic representations of powers of 2

Abstract

A positive integer is \emph{palindromic in the base } when , ,and , Focusing on powers of 2, we investigate the smallest base when is palindromic in the base .
Paper Structure (5 sections, 14 theorems, 35 equations, 5 tables)

This paper contains 5 sections, 14 theorems, 35 equations, 5 tables.

Table of Contents

  1. Introduction
  2. New Results
  3. Some Extensions
  4. Concluding remarks
  5. Acknowledgements

Key Result

Theorem 1.1

If $b(N) = N-1$, then $N=3,4,6$ or $N>6$ and is a prime.

Theorems & Definitions (28)

  • Remark
  • Theorem 1.1: K. Brown Brown
  • proof
  • Remark
  • Lemma 1.2
  • Corollary 1.3
  • proof
  • Lemma 2.1
  • proof
  • Lemma 2.2
  • ...and 18 more