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
Taiwan
Abstract:
A Horadam sequence is a sequence generated by the second-order
linear homogeneous recurrence relation Wn =
pWn−1 − qWn−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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