A072124 a(n)-th factorial is the smallest factorial containing exactly n 1's, or 0 if no such number exists.

1, 14, 19, 25, 32, 40, 33, 60, 63, 47, 68, 64, 74, 87, 79, 73, 97, 110, 107, 132, 134, 129, 116, 136, 123, 113, 145, 143, 160, 180, 153, 171, 185, 176, 224, 209, 196, 207, 229, 221, 211, 167, 236, 252, 260, 201, 235, 274, 249, 231, 246, 284, 199, 273, 294, 267

Offset

1,2

Comments

By checking the factorials of all the numbers below 10^6, it is conjectured that up to 10^4 there are 746 values of n for which a(n) = 0: n = 84, 164, 167, 169, 182, ... (see the link for more values). - Amiram Eldar, Sep 01 2020

Links

Amiram Eldar, Table of n, a(n) for n = 1..83

Amiram Eldar, Table of n, a(n) for n=1..10000 with 746 conjectured values

Example

a(2) = 14 since the 14th factorial, i.e., 14! = 87178291200, contains exactly two 1's.

Mathematica

Do[k = 1; While[ Count[IntegerDigits[k! ], 1] != n, k++ ]; Print[k], {n, 1, 60}]
Module[{f=Table[{n, DigitCount[n!, 10, 1]}, {n, 500}]}, Table[SelectFirst[ f, #[[2]] == k&], {k, 60}]][[All, 1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 27 2019 *)

Crossrefs

Cf. A000142, A072295, A072220, A072208, A072204, A072200, A072199, A072178, A072177, A072163.

Sequence in context: A013657 A013653 A360169 * A026287 A028396 A120158

Adjacent sequences: A072121 A072122 A072123 * A072125 A072126 A072127

Keyword

base,nonn

Author

Shyam Sunder Gupta, Jul 30 2002

Extensions

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

Status

approved