Geodesic
Fibonacci \(s\)-Cullen and \(s\)-Woodall numbers
Journal of integer sequences, Tome 18 (2015) no. 1
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 
@article{JIS_2015__18_1_a1,
     author = {Chaves,  Ana Paula and Marques,  Diego},
     title = {Fibonacci {\(s\)-Cullen} and {\(s\)-Woodall} numbers},
     journal = {Journal of integer sequences},
     year = {2015},
     volume = {18},
     number = {1},
     zbl = {1310.11020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_1_a1/}
}
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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/