On Generalized Cullen and Woodall Numbers That are Also Fibonacci Numbers
Departamento de Matemática
Universidade de Brasília
The m-th Cullen number Cm
is a number of the form
m2m + 1 and the m-th
Woodall number Wm has the form
m2m - 1. In 2003, Luca and
proved that the largest Fibonacci number in the Cullen sequence is
3 and that
F1 = F2 = 1
are the largest Fibonacci numbers in the Woodall
sequence. A generalization of these sequences is defined by
Cm,s = m sm + 1
Wm,s = m sm - 1
for s > 1. In this paper, we search for Fibonacci
numbers belonging to these generalized Cullen and Woodall sequences.
Full version: pdf,
(Concerned with sequences
Received April 9 2014;
revised versions received August 11 2014; August 15 2014.
Published in Journal of Integer Sequences, September 3 2014.
Journal of Integer Sequences home page