Blog Archives

7x ± 1: Close Relative of the Collatz Problem

Barina David

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 the Collatz function. The conjecture is supported by a heuristic argument and computational results.

Analytical Representations of Divisors of Integers

Maślanka Krzysztof

Certain analytical expressions which ”feel“ the divisors of natural numbers are investigated. It is shown that these expressions encode to some extent the well-known algorithm of the sieve of Eratosthenes.

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