Related papers: Concatenated Fibonacci and Lucas numbers do not fo…

The paper has been withdrawn due to a crucial error in section 3.

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The paper has been withdrawn by the author, due to it being fundamentally flawed. The author apologizes for any inconvenience it may have caused.

This paper has been withdrawn because there is a fundamental error in the computations; with the right computational scheme it seems to be just a version of the Jones polynomial

This paper has been withdrawn due to a sign error in the equation for F_11 which invalidates many results.

The paper has been withdrawn by the author due to a crucial error.

This paper has been withdrawn due to crucial erros in equations (24)--(31).

This paper has been withdrawn by the author due to the presented idea is wrong.

This paper has been withdrawn by the author due to a crucial sign error in Proposition 3.1.

In this paper, by presenting bi-periodic Lucas numbers as a binomial sum, we introduce the bi-periodic incomplete Lucas numbers. After that, by using the bi-periodic incomplete Lucas numbers, we derive the recurrence relation and the…

We study the concatenated Fibonacci constant $\mathcal{F} := 0.F_{1}F_{2}F_{3}\cdots = 0.11235813\cdots$, obtained by concatenating the Fibonacci numbers in the fractional part, and ask whether it is normal. We show that several classical…

This paper has been withdrawn by the authors due to the crucial wrong assumption following Eq. 9.

This paper has been withdrawn because of serious errors.

This paper has been withdrawn due a crucial mistake due to a crucial mistake in the proof of Lemma 2.3.

The paper is withdrawn. The proof has an error and it requires a different approach.

The paper has been withdrawn due to numerical error.

Let $(F_n)_{n\geq 0}$ and $(L_n)_{n\geq 0}$ be the Fibonacci and Lucas sequences, respectively. In this paper we determine all Fibonacci numbers which are mixed concatenations of a Fibonacci and a Lucas numbers. By mixed concatenations of $…

In part 1 of this paper some linear weighted generalized Fibonacci number summation identities were derived using the fact that the Fibonacci number is the residue of a rational function. In this part, using the same method, some quadratic…

In this study, we define a new type of Fibonacci and Lucas num- bers which are called bicomplex Fibonacci and bicomplex Lucas numbers. We obtain the well-known properties e.g. Docagnes, Cassini, Catalan for these new types. We also give the…

This paper has been withdrawn by the author because Lemma 3 is incorrect. This mistake is crucial in this paper.