Geodesic
Fibonacci $s$-Cullen and $s$-Woodall numbers
Journal of integer sequences, Tome 18 (2015) no. 1.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: The $m$-th Cullen number $Cm$ is a number of the form $m2^{m} + 1$ and the $m$-th Woodall number $Wm$ has the form $m2^{m} - 1$ In 2003, Luca and Stănică proved that the largest Fibonacci number in the Cullen sequence is $F_{4} = 3$ and that $F_{1} = F_{2} = 1$ are the largest Fibonacci numbers in the Woodall sequence. Very recently, the second author proved that, for any given $s > 1$, the equation $F_{n} = ms^{m} \pm 1$ has only finitely many solutions, and they are effectively computable. In this note, we shall provide the explicit form of the possible solutions.
Classification : 11B39
Keywords: Fibonacci number, cullen number 
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     author = {Chaves, Ana Paula and Marques, Diego},
     title = {Fibonacci $s${-Cullen} and $s${-Woodall} numbers},
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Chaves, Ana Paula; Marques, Diego. Fibonacci $s$-Cullen and $s$-Woodall numbers. Journal of integer sequences, Tome 18 (2015) no. 1. http://geodesic.mathdoc.fr/item/JIS_2015__18_1_a1/