12 citations · 17 across the 9 of their papers we have counts for
12 papers
Products of integers with few nonzero digits
Hajime Kaneko, Thomas Stoll
Let be the number of nonzero bits in the binary digital expansion of the integer . We study, for fixed , the Diophantine system $$ s(ab)=k, \quad s(a)=\ell,\qua…
Maximum order complexity of the sum of digits function in Zeckendorf base and polynomial subsequences
Damien Jamet, Pierre Popoli, Thomas Stoll
Automatic sequences are not suitable sequences for cryptographic applications since both their subword complexity and their expansion complexity are small, and their correlation me…
Discrete correlations of order 2 of generalised Rudin-Shapiro sequences: a combinatorial approach
Irène Marcovici, Thomas Stoll, Pierre-Adrien Tahay
We introduce a family of block-additive automatic sequences, that are obtained by allocating a weight to each couple of digits, and defining the th term of the sequence as being…
The sum-of-digits function on arithmetic progressions
Lukas Spiegelhofer, Thomas Stoll
Let be the sum-of-digits function in base , which returns the number of non-zero binary digits of a nonnegative integer . We study alon g arithmetic subsequences…
On subwords in the base- expansion of polynomial and exponential functions
Hajime Kaneko, Thomas Stoll
Let be any word over the alphabet , and denote by either a polynomial of degree or for a fixed . Furthermore, denote by…
Hensel's lemma for general continuous functions
Hajime Kaneko, Thomas Stoll
In the present paper, we generalize the well-known Hensel's lifting lemma to any continuous function . This answers a question posed by Ax…
On a conjecture of Dekking : The sum of digits of even numbers
Iurie Boreico, Daniel El-Baz, Thomas Stoll
Let and denote by the sum-of-digits function in base . For consider $$# \{0 \le n < N : \;\;s_q(2n) \equiv j \pmod q \}.$$ In 1983, F. M. Dekking…
The sum of digits of polynomial values in arithmetic progressions
Thomas Stoll
Let be integers with . Denote by the sum of digits of in the -ary digital expansion. Further let be a polynomial of d…
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)…
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…
A fancy way to obtain the binary digits of
Thomas Stoll
R. L. Graham and H. O. Pollak observed that the sequence has the curious property that the sequence of nu…
Bounds for the discrete correlation of infinite sequences on k symbols and generalized Rudin-Shapiro sequences
E. Grant, J. Shallit, T. Stoll
Motivated by the known autocorrelation properties of the Rudin-Shapiro sequence, we study the discrete correlation among infinite sequences over a finite alphabet, where we just ta…