The fibonorial 
,
also called the Fibonacci factorial, is defined as
where 
is a Fibonacci
number. For 
,
2, ..., the first few fibonorials are 1, 1, 2, 6, 30, 240, 3120, 65520, ... (OEIS
A003266).
The fibonorials are asymptotic to
where 
is the Fibonacci
factorial constant and 
is the golden ratio.
The first few values of 
such that 
is prime are given by 4, 5, 6, 7, 8, 14, 15, ... (OEIS A059709),
with no others less than 500.
The first few values of 
such that 
is prime are given by 1, 2, 3, 4, 5, 6, 7, 8, 22, 28, ... (OEIS A053408),
with no others less than 500.
See also
Factorial,
Fibonacci Factorial Constant,
Fibonacci Number,
Fibonomial Coefficient,
Integer
Sequence Primes,
Primorial
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References
Brousseau, A. Fibonacci and Related Number Theoretic Tables. San Jose, CA: Fibonacci Association,
p. 69, 1972.Finch, S. R. "Fibonacci Factorials."
§1.2.5 in Mathematical
Constants. Cambridge, England: Cambridge University Press, p. 10, 2003.Graham,
R. L.; Knuth, D. E.; and Patashnik, O. Concrete
Mathematics: A Foundation for Computer Science, 2nd ed. Reading, MA: Addison-Wesley,
p. 597, 1994.Matiyasevich, Y. V. and Guy, R. K. "A
New Formula for Pi." Amer. Math. Monthly 93, 631-635, 1986.Sloane,
N. J. A. Sequences A003266/M1692,
A053408, and A059709
in "The On-Line Encyclopedia of Integer Sequences."Referenced
on Wolfram|Alpha
Fibonorial
Cite this as:
Weisstein, Eric W. "Fibonorial." From
MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Fibonorial.html
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