Primitive quadratics reflected in -sequences.
Propriétés additives des suites et de leurs carrés
Pseudoprime Cullen and Woodall numbers
We show that if a > 1 is any fixed integer, then for a sufficiently large x>1, the nth Cullen number Cₙ = n2ⁿ +1 is a base a pseudoprime only for at most O(x log log x/log x) positive integers n ≤ x. This complements a result of E. Heppner which asserts that Cₙ is prime for at most O(x/log x) of positive integers n ≤ x. We also prove a similar result concerning the pseudoprimality to base a of the Woodall numbers given by Wₙ = n2ⁿ - 1 for all n ≥ 1.
-extensions for the Apostol–Genocchi polynomials.
q-Stern Polynomials as Numerators of Continued Fractions
We present a q-analogue for the fact that the nth Stern polynomial Bₙ(t) in the sense of Klavžar, Milutinović and Petr [Adv. Appl. Math. 39 (2007)] is the numerator of a continued fraction of n terms. Moreover, we give a combinatorial interpretation for our q-analogue.
Quasi-Fibonacci numbers of order 11.
Quasi-Fibonacci numbers of the seventh order.
Ramanujan type trigonometric formulas: the general form for the argument .
Rectangular and trapezoidal arrangements.
Recurrences and Legendre transform.
Reducibility and irreducibility of Stern -polynomials
The classical Stern sequence was extended by K.B. Stolarsky and the first author to the Stern polynomials defined by , , , and ; these polynomials are Newman polynomials, i.e., they have only 0 and 1 as coefficients. In this paper we prove numerous reducibility and irreducibility properties of these polynomials, and we show that cyclotomic polynomials play an important role as factors. We also prove several related results, such as the fact that can only have simple zeros, and we state a...
Regularity and irregularity of sequences generated by automata
Regularity properties of the Stern enumeration of the rationals.
Remarks on number theory III. On addition chains
Remarks on Steinhaus’ property and ratio sets of sets of positive integers
This paper is closely related to an earlier paper of the author and W. Narkiewicz (cf. [7]) and to some papers concerning ratio sets of positive integers (cf. [4], [5], [12], [13], [14]). The paper contains some new results completing results of the mentioned papers. Among other things a characterization of the Steinhaus property of sets of positive integers is given here by using the concept of ratio sets of positive integers.
Répartition des sous-suites d'une suite donnée
Répartition des sous-suites d'une suite donnée
Résultants cycliques et polynômes cyclotomiques
Résultats et problèmes en théorie des nombres
Riordan arrays, orthogonal polynomials as moments, and Hankel transforms.