A332842 Initial digit of n-th superfactorial.

1, 1, 2, 1, 2, 3, 2, 1, 5, 1, 6, 2, 1, 7, 6, 9, 1, 6, 4, 5, 1, 6, 7, 1, 1, 1, 7, 7, 2, 2, 5, 4, 1, 1, 3, 3, 1, 1, 8, 1, 1, 4, 6, 4, 1, 1, 7, 1, 2, 1, 4, 6, 5, 2, 5, 6, 4, 1, 4, 6, 5, 2, 8, 1, 2, 1, 9, 3, 8, 1, 1, 1, 9, 4, 1, 3, 6, 9, 1, 9, 6, 3, 1, 7, 2, 6, 1, 3, 6, 1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2

Offset: 0

Author

Eder Vanzei, Feb 26 2020

Keywords

• easy
• nonn
• base

Examples

			a(6) = 2 because A000178(6) = 24883200.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000030, A000178, A008905.

Programs

PARI

a(n) = digits(prod(k=2, n, k!))[1]; \\ Michel Marcus, Feb 26 2020

Python

def A332842(n):
    m, k = 1, 1
    for i in range(2,n+1):
        k *= i
        m *= k
    return int(str(m)[0]) # Chai Wah Wu, Mar 17 2020

Formula

a(n) = A000030(A000178(n)).