Sums of the Thue-Morse Sequence over Arithmetic Progressions

Abstract

In this note, we use the theory of Boolean functions to find a new elementary proof for Moser's conjecture that states that in the bounded sequence of nonnegative integers divisible by 3 there are more integers with an even number of 1s in their base-2 representation. This proof is simpler than the original proof by D. J. Newman in 1969. We further apply the method to prove a similar result for p = 5, which was also done by Grabner in 1993. The method seems to be extendable to other primes, but the computations for the relevant constants will be quite complex.

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Document Details

Document Type
Technical Report
Publication Date
May 29, 2009
Accession Number
ADA548760

Entities

People

  • P. Stanica
  • T. W. Cusick

Organizations

  • Naval Postgraduate School

Tags

DTIC Thesaurus Topics

  • Applied Mathematics
  • Arithmetic
  • Complex Variables
  • Computations
  • Functions (Mathematics)
  • Information Operations
  • Mathematical Analysis
  • Mathematics
  • New York
  • Periodic Functions
  • Sequences
  • Sequences (Mathematics)
  • Special Functions (Mathematics)
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.