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$7x\pm1$: Close Relative of Collatz Problem

David Barina

Abstract

We show an iterated function of which iterates oscillate wildly and grow at a dizzying pace. We conjecture that the orbit of arbitrary positive integer always returns to 1, as in the case of Collatz function. The conjecture is supported by a heuristic argument and computational results.

$7x\pm1$: Close Relative of Collatz Problem

Abstract

We show an iterated function of which iterates oscillate wildly and grow at a dizzying pace. We conjecture that the orbit of arbitrary positive integer always returns to 1, as in the case of Collatz function. The conjecture is supported by a heuristic argument and computational results.

Paper Structure

This paper contains 3 equations, 2 figures, 7 tables.

Figures (2)

  • Figure 1: $7x\pm1$ sequence starting at 235. Due to a very large number range, the sequence in linear scale is shown on top, in logarithmic scale on the bottom.
  • Figure 2: Numbers 1 to 10 000 and their total stopping time. The $3x+1$ on top, the $7x\pm1$ on the bottom.