Journal of Integer Sequences, Vol. 17 (2014), Article 14.9.4

On Generalized Cullen and Woodall Numbers That are Also Fibonacci Numbers

Diego Marques
Departamento de Matemática
Universidade de Brasília
Brasília 70910-900


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 Stănică proved that the largest Fibonacci number in the Cullen sequence is F4 = 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 and 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,    dvi,    ps,    latex    

(Concerned with sequences A000045 A002064 A003261.)

Received April 9 2014; revised versions received August 11 2014; August 15 2014. Published in Journal of Integer Sequences, September 3 2014.

Return to Journal of Integer Sequences home page