Special factorials: Difference between revisions

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==((header|Julia}}==

No recursion.

<lang julia># No recursion.

superfactorial(n) = n < 1 ? 1 : mapreduce(factorial, *, 1:n)

sf(n) = superfactorial(n)

hyperfactorial(n) = n < 1 ? 1 : mapreduce(i -> i^i, *, 1:n)

H(n) = hyperfactorial(n)

alternating_factorial(n) = n < 1 ? -1 : mapreduce(i -> (-1)^(n - i) * factorial(i), +, 1:n)

af(n) = alternating_factorial(n)

exponential_factorial(n) = n < 1 ? 1 : foldl((x, y) -> y^x, 1:n)

n＄(n) = exponential_factorial(n)

function reverse_factorial(n)

for i in 1:100000

fac = factorial(typeof(n)(i))

fac == n && return i

fac > n && break

end

return nothing

end

rf(n) = reverse_factorial(n)

println("N Superfactorial Hyperfactorial Alternating Factorial Exponential Factorial\n", "-"^88)

for n in 0:9

print(n, " ")

for f in [sf, H, af, n＄]

if n < 5 || f != n＄

print(rpad((f(n)), 25))

end

end

println()

end

println("\nThe number of digits in n＄(5) is ", length(string(n＄(BigInt(5)))))

println("\n\nN Reverse Factorial\n", "-"^25)

for n in [1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 119]

println(rpad(n, 10), rf(n))

end

</lang>{{out}}

<pre>

N Superfactorial Hyperfactorial Alternating Factorial Exponential Factorial

----------------------------------------------------------------------------------------

0 1 1 -1 1

1 1 1 1 1

2 2 4 1 2

3 12 108 5 9

4 288 27648 19 262144

5 34560 86400000 101

6 24883200 4031078400000 619

7 125411328000 3319766398771200000 4421

8 5056584744960000 -907465429310504960 35899

9 8705808953839190016 2649120435010011136 326981

The number of digits in n＄(5) is 183231

N Reverse Factorial

-------------------------

1 1

2 2

6 3

24 4

120 5

720 6

5040 7

40320 8

362880 9

3628800 10

119 nothing