Terme général d'une série quelconque déterminée à la façon des séries récurrentes
Terms in elliptic divisibility sequences divisible by their indices
The conjugacy map over a Sturmian word.
The problem as a string rewriting system.
The Collatz problem and analogues.
The combinatorialization of linear recurrences.
The combinatorics of certain -ary meta-Fibonacci sequences.
The D(1)-extensions of D(-1)-triples 1,2,c and integer points on the attached elliptic curves
The Diophantine equation
It is shown that for a given squarefree positive integer D, the equation of the title has no solutions in integers x > 0, m > 0, n ≥ 3 and y odd, nor unless D ≡ 14 (mod 16) in integers x > 0, m = 0, n ≥ 3, y > 0, provided in each case that n does not divide the class number of the imaginary quadratic field containing √(-2D), except for a small number of (stated) exceptions.
The diophantine equations .
The distance between terms of an algebraic recurrence sequence.
The distribution of trees.
The distribution of the sum-of-digits function
By using a generating function approach it is shown that the sum-of-digits function (related to specific finite and infinite linear recurrences) satisfies a central limit theorem. Additionally a local limit theorem is derived.
The equation and related dispersions.
The equation x+y=1 in finitely generated groups
The greatest common divisor of two recursive functions.
The intersection of recurrence sequences
The Josephus problem
We give explicit non-recursive formulas to compute the Josephus-numbers and and explicit upper and lower bounds for (where ) which differ by (for the bounds are even better). Furthermore we present a new fast algorithm to calculate which is based upon the mentioned bounds.
The multiplicity of binary recurrences
The Pell Sequence of Order K, Multinomial Coefficients, and Probability