The density of numbers \(n\) having a prescribed G.C.D. with the \(n\)th Fibonacci number
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Publication:1749025
DOI10.1016/j.indag.2018.03.002zbMath1417.11012arXiv1705.01805OpenAlexW2963605982MaRDI QIDQ1749025
Publication date: 15 May 2018
Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1705.01805
greatest common divisorFibonacci numbersasymptotic densitynon-degenerate Lucas sequencerank of appearance
Density, gaps, topology (11B05) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05)
Related Items (8)
The moments of the logarithm of a G.C.D. related to Lucas sequences ⋮ Greatest common divisors of shifted primes and Fibonacci numbers ⋮ On the greatest common divisor of n and the nth Fibonacci number, II ⋮ On numbers \(n\) relatively prime to the \(n\)th term of a linear recurrence ⋮ ON NUMBERS WITH POLYNOMIAL IMAGE COPRIME WITH THE TH TERM OF A LINEAR RECURRENCE ⋮ An upper bound for the moments of a GCD related to Lucas sequences ⋮ The density of the terms in an elliptic divisibility sequence having a fixed G.C.D. with their indices ⋮ On terms in a dynamical divisibility sequence having a fixed g.c.d with their indices
Cites Work
- On the greatest common divisor of \(n\) and the \(n\)th Fibonacci number
- Period of the power generator and small values of Carmichael’s function
- The Distribution of Self-Fibonacci Divisors
- On the sumset of the primes and a linear recurrence
- The Period, Rank, and Order of the (a, b)-Fibonacci Sequence Mod m
- On numbers n dividing the nth term of a linear recurrence
- On numbers n dividing the nth term of a Lucas sequence
- ON THE SUM OF A PRIME AND A FIBONACCI NUMBER
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