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Proofs of some Conjectures from the OEIS

Sela Fried

Abstract

In this work we resolve several conjectures stated in the On-Line Encyclopedia of Integer sequences.

Proofs of some Conjectures from the OEIS

Abstract

In this work we resolve several conjectures stated in the On-Line Encyclopedia of Integer sequences.

Paper Structure

This paper contains 11 sections, 12 theorems, 57 equations.

Table of Contents

  1. Introduction
  2. Main results
  3. The number of bits required to represent
  4. Floor of sum of the first cube roots
  5. Median absolute deviation of
  6. The integer lattice and its layers
  7. Maximum value of a cyclic convolution
  8. The real part of a recursively defined complex sequence
  9. The generating functions of two sequences
  10. Words avoiding the patters and
  11. A greedily defined integer sequence

Key Result

Theorem 1

Let $n\geq 1$ be an integer. The number of binary bits required to represent $\binom{2^n}{2^{n-1}}$ is $2^n -\lfloor n/2\rfloor$.

Theorems & Definitions (23)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • proof
  • Theorem 4
  • proof
  • Corollary 5
  • proof
  • ...and 13 more