k-generalized Fibonacci numbers of the form 1+2^{n_1}+4^{n_2}+\cdots+(2^{k})^{n_k}
Ruiz, Carlos Alexis Gómez ; Luca, Florian
Mathematical Communications, Tome 19 (2014) no. 1, p. 321-332 / Harvested from Mathematical Communications
Text on Mathematical Communications
A generalization of the well-known Fibonacci sequence is the k-generalized Fibonacci sequence (F_n^{(k)})_{n>= 2-k} whose first k terms are 0, ..., 0, 1 and each term afterwards is the sum of the preceding k terms. In this paper, we investigate k-generalized Fibonacci numbers written in the form 1+2^{n_1}+4^{n_2}+\cdots+(2^{k})^{n_k}, for non-negative integers n_i, with n_k >= max{ n_i | 1<= i <= k-1}.
Publié le : 2014-10-26
Classification:  Fibonacci numbers, Lower bounds for nonzero linear forms in logarithms of algebraic numbers,  11B39; 11J86 
@article{mc569,
     author = {Ruiz, Carlos Alexis G\'omez and Luca, Florian},
     title = {k-generalized Fibonacci numbers of the form 1+2^{n\_1}+4^{n\_2}+\cdots+(2^{k})^{n\_k}},
     journal = {Mathematical Communications},
     volume = {19},
     number = {1},
     year = {2014},
     pages = { 321-332},
     language = {eng},
     url = {http://dml.mathdoc.fr/item/mc569}
}

Ruiz, Carlos Alexis Gómez; Luca, Florian. k-generalized Fibonacci numbers of the form 1+2^{n_1}+4^{n_2}+\cdots+(2^{k})^{n_k}. Mathematical Communications, Tome 19 (2014) no. 1, pp.  321-332. http://gdmltest.u-ga.fr/item/mc569/