Journal of Integer Sequences, Vol. 23 (2020), Article 20.5.8

Greatest Common Divisors of Shifted Horadam Sequences

Kwang-Wu Chen and Yu-Ren Pan
Department of Mathematics
University of Taipei
No. 1, Aiguo West Road
Taipei 10048


A Horadam sequence is a sequence generated by the second-order linear homogeneous recurrence relation Wn = pWn−1qWn−2; W0 = a, W1 = b. The sequence of Fibonacci numbers is a particular case of a Horadam sequence. For any fixed integers s, t, and k, we investigate the boundedness and periodicity of the sequence (gcd(Wn + s, Wn+k + t)) in this paper.

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(Concerned with sequences A000032 A000045 A000129 A001110 A001541 A002203.)

Received July 1 2019; revised version received March 12 2020; April 3 2020. Published in Journal of Integer Sequences, June 8 2020.

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