A332242 Numbers k such that k! has exactly k nonzero decimal digits.

1, 48, 49, 53, 54, 57

Offset: 1

Author

Chai Wah Wu, Feb 07 2020

Keywords

• nonn
• base

Comments

No other terms < 100000.

Conjecture: these 6 terms are the only terms of the sequence, i.e., there are no terms larger than 57.

Examples

			48! = 12413915592536072670862289047373375038521486354677760000000000 has 48 nonzero decimal digits, so 48 is a term.
		

Crossrefs

Cf. A000142, A027869, A034886.

Programs

Maple

q:= n-> nops(subs(0=NULL, convert(n!, base, 10)))=n:
select(q, [$0..100])[];  # Alois P. Heinz, Feb 07 2020

PARI

isok(k) = #select(x->(x != 0), digits(k!)) == k; \\ Michel Marcus, Feb 08 2020

Python

A332242_list, i, n = [], 0, 1
while i < 1000:
    s = str(n)
    if len(s) - s.count('0') == i:
        A332242_list.append(i)
    i += 1
    n *= i

Formula

{ k : A034886(k) - A027869(k) = k }.