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

1,2

Links

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

Formula

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

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A198376 (largest), A002473, A068191.

Sequence in context: A153882 A357650 A322649 * A124651 A231379 A237855

Adjacent sequences: A198372 A198373 A198374 * A198376 A198377 A198378

Keyword

nonn,base

Author

Jaroslav Krizek, Oct 23 2011

Status

approved