Fibonorial

From Wikipedia, the free encyclopedia
Jump to: navigation, search

In mathematics, the Fibonorial n!F, also called the Fibonacci factorial, where n is a nonnegative integer, is defined as the product of the first n positive Fibonacci numbers, i.e.

{n!}_F := \prod_{i=1}^{n} F_i,\quad n \ge 1, \text{ and } 0!_F := 1,

where Fi is the ith Fibonacci number. (0!F is 1 since it is the empty product.)

The Fibonorial of n (n!F) is defined analogously to the factorial of n (n!).

The Fibonorial numbers are used in the definition of Fibonomial coefficients (or Fibonacci-binomial coefficients) similarly as the factorial numbers are used in the definition of binomial coefficients.

Almost-Fibonorial numbers[edit]

Almost-Fibonorial numbers: n!F − 1.

It is interesting to look for prime numbers among the almost-Fibonorial numbers, i.e. the almost-Fibonorial primes.

Quasi-Fibonorial numbers[edit]

Quasi-Fibonorial numbers: n!F + 1.

It is interesting to look for prime numbers among the quasi-Fibonorial numbers, i.e. the quasi-Fibonorial primes.

Sequences[edit]

Cf. OEISA003266 Product of first n nonzero Fibonacci numbers F(1), ..., F(n).

Cf. OEISA059709 and OEISA053408 for n such that n!F − 1 and n!F + 1 are primes.

References[edit]

  • Weisstein, Eric W. "Fibonorial". MathWorld. Wolfram Research. Retrieved 19 December 2009.