There are a number of possible generalizations of the Fibonacci numbers which include the real numbers (and sometimes the complex numbers) in their domain...

mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones. Numbers that are part of the Fibonacci sequence are...

integers based on Fibonacci numbers. Each code word ends with "11" and contains no other instances of "11" before the end. The Fibonacci code is closely...

sequence of Fibonacci numbers taken modulo n repeats. Pisano periods are named after Leonardo Pisano, better known as Fibonacci. The existence of periodic...

mathematics, the Fibonacci polynomials are a polynomial sequence which can be considered as a generalization of the Fibonacci numbers. The polynomials...

closely related Fibonacci sequence. Individual numbers in the Lucas sequence are known as Lucas numbers. Lucas numbers and Fibonacci numbers form complementary...

concatenation in the same way that the Fibonacci numbers are formed by repeated addition. It is a paradigmatic example of a Sturmian word and specifically,...

such as the sequence of Fibonacci numbers, the sequence of factorials, the sequence of perfect numbers, and so forth, many of which are enumerated in...

This is a list of articles about prime numbers. A prime number (or prime) is a natural number greater than 1 that has no positive divisors other than...

"Benford's Law for Fibonacci and Lucas Numbers". The Fibonacci Quarterly. 19 (2): 175–177. Duncan, R. L. (1967). "An Application of Uniform Distribution...

In mathematics, the random Fibonacci sequence is a stochastic analogue of the Fibonacci sequence defined by the recurrence relation f n = f n − 1 ± f n...

values of k {\displaystyle k} , the constants are related to generalizations of Fibonacci numbers such as the tribonacci and tetranacci numbers. The corresponding...

natural numbers such that a × b = 0, then a = 0 or b = 0 (or both). Two important generalizations of natural numbers arise from the two uses of counting...

them. Example of such sets of integers are Fibonacci numbers and perfect numbers. For more examples, see Integer sequence. Algebraic numbers are those that...

The prime numbers are widely used in mathematics, particularly in number theory where many results related to them exist. The Fibonacci numbers comprise...

c^{2}Q)=c^{n}\cdot V_{n}(P,Q).} The terms of Lucas sequences satisfy relations that are generalizations of those between Fibonacci numbers F n = U n ( 1 , − 1 ) {\displaystyle...

Iekata (1997). "Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibonacci numbers". Proceedings of the Japan Academy, Series A...

The Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. They are named...

is the number of nodes. The idea of this algorithm is also given in Leyzorek et al. 1957. Fredman & Tarjan 1984 proposed using a Fibonacci heap priority...

Encyclopedia of Integer Sequences. OEIS Foundation. Waddill, Marcellus E. (1992), "The Tetranacci sequence and generalizations" (PDF), The Fibonacci Quarterly...

28, 8) = 2. This result in turn has further generalizations. The two sets of three numbers which the Star of David theorem says have equal greatest common...

N steps for a pair of natural numbers a > b > 0, the smallest values of a and b for which this is true are the Fibonacci numbers FN+2 and FN+1, respectively...

explanation of LFSRs for Engineers Feedback terms General LFSR Theory An implementation of LFSR in VHDL. Simple VHDL coding for Galois and Fibonacci LFSR. mlpolygen:...

sequential Fibonacci numbers, suggesting a generalization of the dissection scheme based on Fibonacci numbers. The properties of the Fibonacci numbers also...

that the sieve of Eratosthenes can be sped up by considering only the prime divisors up to the square root of the upper limit. Fibonacci took the innovations...

result of the multiplication. Systematic generalizations of this basic definition define the multiplication of integers (including negative numbers), rational...

István Mező (2008). "A Symmetric Algorithm for Hyperharmonic and Fibonacci Numbers". Applied Mathematics and Computation. 206 (2): 942–951. arXiv:0803...

autosequence is of the first kind. Example: OEIS: A000045, the Fibonacci numbers. If the main diagonal is the first upper diagonal multiplied by 2, it is of the second...

non-consecutive Fibonacci numbers. Complete sequence Allouche, Jean-Paul; Shallit, Jeffrey (2003). Automatic Sequences: Theory, Applications, Generalizations. Cambridge...

Amicable numbers are two different natural numbers related in such a way that the sum of the proper divisors of each is equal to the other number. That...