A072178 a(n)-th factorial is the smallest factorial containing exactly n 4's, or 0 if no such number exists.

4, 19, 21, 24, 44, 42, 50, 57, 0, 60, 76, 91, 56, 86, 85, 66, 92, 88, 114, 129, 131, 106, 130, 122, 117, 157, 134, 175, 119, 150, 181, 165, 185, 179, 198, 182, 220, 228, 188, 190, 261, 235, 222, 231, 229, 233, 224, 227, 288, 372, 241, 279, 254, 253, 318, 267

Offset

1,1

Comments

It is conjectured that a(9) = 0 since no factorial < 10000 contained just 9 fours.

Links

Table of n, a(n) for n=1..56.

Example

a(2) = 19 since 19th factorial, i.e., 19! = 121645100408832000 contains exactly two 4's.

Mathematica

Do[k = 1; While[ Count[IntegerDigits[k! ], 4] != n, k++ ]; Print[k], {n, 1, 60}]

Prog

(Python)
from math import factorial
def a(n, limit=1000):
  fact = 1
  for t in range(limit+1):
    if str(fact).count('4') == n: return t
    fact *= (t+1)
  return 0
print([a(n) for n in range(1, 57)]) # Michael S. Branicky, Apr 19 2021

Crossrefs

Cf. A072244, A072220, A072208, A072204, A072200, A072199, A072177, A072163, A072124.

Sequence in context: A165820 A043056 A012879 * A116980 A296602 A022135

Adjacent sequences: A072175 A072176 A072177 * A072179 A072180 A072181

Keyword

base,nonn

Author

Shyam Sunder Gupta, Jul 30 2002

Extensions

Edited and extended by Robert G. Wilson v, Jul 31 2002

Status

approved