Sagan numbers

TL;DR

Sagan numbers are a new class of numbers defined by the first occurrence of specific binary patterns in the expansions of irrational numbers, inspired by Carl Sagan's mention in his novel, with connections to various mathematical concepts.

Contribution

The paper introduces Sagan numbers, a novel concept linking pattern occurrences in irrational number expansions to mathematical ideas, inspired by literature.

Findings

Defined properties of Sagan numbers

Connected Sagan numbers to existing mathematical concepts

Suggested future research directions

Abstract

We define a new class of numbers based on the first occurrence of certain patterns of zeros and ones in the expansion of irracional numbers in a given basis and call them Sagan numbers, since they were first mentioned, in a special case, by the North-american astronomer Carl E. Sagan in his science-fiction novel "Contact." Sagan numbers hold connections with a wealth of mathematical ideas. We describe some properties of the newly defined numbers and indicate directions for further amusement.