Generalizations of Fibonacci numbers information

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...

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

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

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,...

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

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...

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...

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

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...

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

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...

any expression. Prime numbers Sequences Fibonacci numbers Generalizations of Fibonacci numbers Geometric progressions Difference sequences Recurrence relations...

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...

representations of its two factors, using the Brahmagupta–Fibonacci identity. Jacobi's two-square theorem states The number of representations of n as a sum of two...

objects constructed from integers (for example, rational numbers), or defined as generalizations of the integers (for example, algebraic integers). Integers...

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...

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

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...

In combinatorial mathematics, the Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively...

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...

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