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math.NT2021★ 1 cited
Primes as sums of Fibonacci numbers
Michael Drmota, Clemens Müllner, Lukas Spiegelhofer
The purpose of this paper is to discuss the relationship between prime numbers and sums of Fibonacci numbers. One of our main results says that for every sufficiently large integer…
math.NT2021
Collisions of digit sums in bases 2 and 3
Lukas Spiegelhofer
We prove a folklore conjecture concerning the sum-of-digits functions in bases two and three: there are infinitely many positive integers such that the sum of the binary digits…
math.CO2021
Gaps in the Thue--Morse word
Lukas Spiegelhofer
The Thue--Morse sequence is a prototypical automatic sequence found in diverse areas of mathematics, and in computer science. We study occurrences of factors within this sequen…