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math.NT2010
Extremal orders of the Zeckendorf sum of digits of powers
Thomas Stoll
Denote by s_F(n) the minimal number of Fibonacci numbers needed to write n as a sum of Fibonacci numbers. We obtain the extremal minimal and maximal orders of magnitude of s_F(n^h)…
math.NT2010
Thue-Morse at Multiples of an Integer
Johannes F. Morgenbesser, Jeffrey Shallit, Thomas Stoll
Let (t_n) be the classical Thue-Morse sequence defined by t_n = s_2(n) (mod 2), where s_2 is the sum of the bits in the binary representation of n. It is well known that for any in…