A198375 Smallest n-digit number whose product of digits is n or 0 if no number exists.

1, 12, 113, 1114, 11115, 111116, 1111117, 11111118, 111111119, 1111111125, 0, 111111111126, 0, 11111111111127, 111111111111135, 1111111111111128, 0, 111111111111111129, 0, 11111111111111111145, 111111111111111111137, 0, 0, 111111111111111111111138

Offset: 1

Author

Jaroslav Krizek, Oct 23 2011

Keywords

• nonn
• base

Examples

			113, 131, and 311 are the 3-digit numbers whose product of digits is 3; 113 is the smallest.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A198376 (largest), A002473, A068191.

Programs

Mathematica

Table[If[FactorInteger[n][[-1, 1]] > 9, 0, i = (10^n - 1)/9; While[i < 10^n && Times @@ IntegerDigits[i] != n, i++]; If[i == 10^n, 0, i]], {n, 30}] (* T. D. Noe, Oct 24 2011 *)

Python

def A198375(n): return int(str(A198376(n))[::-1])
print([A198375(n) for n in range(1, 25)]) # Michael S. Branicky, Jan 21 2021

Formula

a(A068191(n)) = 0 for n >=1.

a(n) <> 0 iff n in { A002473 }. - Michael S. Branicky, Jan 21 2021