A search for Tribonacci-Wieferich primes
Such problems as the search for Wieferich primes or Wall-Sun-Sun primes are intensively studied and often discused at present. This paper is devoted to a similar problem related to the Tribonacci numbers.
A self-indexed sequence.
A self-similar tiling generated by the minimal Pisot number
A sequence adapted from the movement of the center of mass of two planets in solar system
In this paper we derive a sequence from a movement of center of~mass of arbitrary two planets in some solar system, where the planets circle on concentric circles in a same plane. A trajectory of center of mass of the planets is discussed. A sequence of points on the trajectory is chosen. Distances of the points to the origin are calculated and a distribution function of a sequence of the distances is found.
A Sequence Has Almost Nowhere Small Discrepancy.
A sequence of binomial coefficients related to Lucas and Fibonacci numbers.
A Sequence of Exponential Numbers
A sequential Riesz-like criterion for the Riemann Hypothesis.
A series transformation formula and related polynomials.
A set of infinite measure whose ratio set does not contain a given sequence.
A set of squares without arithmetic progressions
A sextuple product identity with applications.
A sharp estimate of the number of integral points in a 4-dimensional tetrahedra.
A sharp estimate of the number of integral points in a tetrahedron.
A sharpening of the bounds for linear forms in logarithms
A sharpening of the bounds for linear forms in logarithms II
A sharpening of the bounds for linear forms in logarithms III
A sharper bound for the least pair of consecutive k-th power non-residues of non-principal characters (mod p) of order k > 3
A short intervals result for linear equations in two prime variables.
Given A and B integers relatively prime, we prove that almost all integers n in an interval of the form [N, N+H], where N exp(1/3+e) ≤ H ≤ N can be written as a sum Ap1 + Bp2 = n, with p1 and p2 primes and e an arbitrary positive constant. This generalizes the results of Perelli et al. (1985) established in the classical case A=B=1 (Goldbach's problem).
A short note on the difference between inverses of consecutive integers modulo .