Journal of Integer Sequences, Vol. 18 (2015), Article 15.1.4

Fibonacci s-Cullen and s-Woodall Numbers

Diego Marques
Departamento de Matemática
Universidade de Brasília
Brasília, Brazil

Ana Paula Chaves
Instituto de Matemática e Estatística
Universidade Federal de Goiás
Goiás, Brazil


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. Very recently, the second author proved that, for any given s > 1, the equation Fn = msm ± 1 has only finitely many solutions, and they are effectively computable. In this note, we shall provide the explicit form of the possible solutions.

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(Concerned with sequences A000045 A002064.)

Received October 11 2014; revised versions received December 24 2014. Published in Journal of Integer Sequences, January 6 2015.

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