A198375 - OEIS

%I #18 Jan 21 2021 11:01:39

%S 1,12,113,1114,11115,111116,1111117,11111118,111111119,1111111125,0,

%T 111111111126,0,11111111111127,111111111111135,1111111111111128,0,

%U 111111111111111129,0,11111111111111111145,111111111111111111137,0,0,111111111111111111111138

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

%H Michael S. Branicky, <a href="/A198375/b198375.txt">Table of n, a(n) for n = 1..1000</a>

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

%F a(n) <> 0 iff n in { A002473 }. - _Michael S. Branicky_, Jan 21 2021

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

%t 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 *)

%o (Python)

%o def A198375(n): return int(str(A198376(n))[::-1])

%o print([A198375(n) for n in range(1, 25)]) # _Michael S. Branicky_, Jan 21 2021

%Y Cf. A198376 (largest), A002473, A068191.

%K nonn,base

%O 1,2

%A _Jaroslav Krizek_, Oct 23 2011