On integer-sequence-based constructions of generalized Pascal triangles.
On -free numbers over Beatty sequences
We consider -free numbers over Beatty sequences. New results are given. In particular, for a fixed irrational number of finite type and any constant , we can show that where is the set of positive -free integers and the implied constant depends only on ...
On multiples of certain real sequences
On permutations containing no long arithmetic progressions
On practical partitions.
On Representing Integers as Products of the p + 1.
On sequences of positive integers
On Sidon sequences of even orders
On some Formulas Involving !n and the Verification of the !n-hypothesis by use of Computers
On some Markov matrices arising from the generalized Collatz mapping
On some properties of Chebyshev polynomials
Letting (resp. ) be the n-th Chebyshev polynomials of the first (resp. second) kind, we prove that the sequences and for n - 2⎣n/2⎦ ≤ k ≤ n - ⎣n/2⎦ are two basis of the ℚ-vectorial space formed by the polynomials of ℚ[X] having the same parity as n and of degree ≤ n. Also and admit remarkableness integer coordinates on each of the two basis.
On sums of distinct representatives
On ternary inclusion-exclusion polynomials.
On the (3N+1)-conjecture
On the central coefficients of Bell matrices.
On the Collatz conjecture
We propose two conjectures which imply the Collatz conjecture. We give a numerical evidence for the second conjecture.
On the difference of consecutive terms of sequences defined by divisibility properties, II
On the difference of consecutive terms of sequences defined by divisibility properties
On the distribution of arithmetic functions
On the distribution of multiplicative arithmetical functions