Thomas Stoll

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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

The sum of digits of $n$ and $n^{2}$

K. G. Hare, S. Laishram, T. Stoll

Let $s_{q} (n)$ denote the sum of the digits in the $q$ -ary expansion of an integer $n$ . In 2005, Melfi examined the structure of $n$ such that $s_{2} (n) = s_{2} (n^{2})$ . We extend this stu…

math.NT2010

Stolarsky's conjecture and the sum of digits of polynomial values

K. G. Hare, S. Laishram, T. Stoll

Let $s_{q} (n)$ denote the sum of the digits in the $q$ -ary expansion of an integer $n$ . In 1978, Stolarsky showed that $n \to \infty lim inf \frac{s _{2} ( n ^{2} )}{s _{2} ( n )} = 0.$ He conj…

Extremal orders of the Zeckendorf sum of digits of powers

The sum of digits of n and n2

Stolarsky's conjecture and the sum of digits of polynomial values

The sum of digits of $n$ and $n^{2}$