A072177 a(n)-th factorial is the smallest factorial containing exactly n 3's, or 0 if no such number exists.

8, 15, 25, 36, 24, 49, 32, 54, 43, 69, 76, 89, 84, 113, 82, 105, 112, 92, 114, 106, 118, 107, 109, 151, 166, 143, 160, 149, 190, 152, 158, 172, 176, 0, 192, 181, 183, 177, 180, 202, 200, 193, 226, 238, 242, 223, 251, 227, 290, 261, 267, 292, 265, 300, 295, 285

Offset

1,1

Comments

It is conjectured that a(34)=0 since no factorial < 10000 contained just 34 threes.

The 500-term b-file contains 16 zeros, each relying on the same conjecture, i.e., that because there is no factorial < 10000! containing just n threes no factorial satisfies the condition. - Harvey P. Dale, Jan 02 2021

Links

Harvey P. Dale, Table of n, a(n) for n = 1..500

Example

a(2)=15 since the 15th factorial, i.e., 15!=1307674368000, contains exactly two 3's.

Mathematica

Do[k = 1; While[ Count[IntegerDigits[k! ], 3] != n, k++ ]; Print[k], {n, 1, 60}]
With[{fc=Range[400]!}, Table[Position[fc, _?(DigitCount[#, 10, 3]==n&), 1, 1]/.{}->0, {n, 60}]]//Flatten (* Harvey P. Dale, Jan 02 2021 *)

Crossrefs

Cf. A072269, A072220, A072208, A072204, A072200, A072199, A072178, A072163 & A072124.

Sequence in context: A069826 A129076 A292949 * A169875 A318111 A240522

Adjacent sequences: A072174 A072175 A072176 * A072178 A072179 A072180

Keyword

base,nonn

Author

Shyam Sunder Gupta, Jul 30 2002

Extensions

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

Status

approved