cp's OEIS Frontend

A068189 Smallest positive number whose product of digits equals n, or a(n)=0 if no such number exists, i.e. when n has a prime divisor greater than 7.

%I A068189 #35 Apr 13 2021 21:05:21
%S A068189 1,2,3,4,5,6,7,8,9,25,0,26,0,27,35,28,0,29,0,45,37,0,0,38,55,0,39,47,
%T A068189 0,56,0,48,0,0,57,49,0,0,0,58,0,67,0,0,59,0,0,68,77,255,0,0,0,69,0,78,
%U A068189 0,0,0,256,0,0,79,88,0,0,0,0,0,257,0,89,0,0,355,0,0,0,0,258,99,0,0,267,0
%N A068189 Smallest positive number whose product of digits equals n, or a(n)=0 if no such number exists, i.e. when n has a prime divisor greater than 7.
%C A068189 a(n) > 0 if and only if n is in A002473.
%H A068189 David A. Corneth, <a href="/A068189/b068189.txt">Table of n, a(n) for n = 1..10000</a>
%e A068189 n=2,10,50,250 gives a(n)=2,25,255,2555; n=11,39,78, etc..a(n)=0.
%e A068189 10000 = 2 * 5 * 5 * 5 * 5 * 8. No product of two of these factors is less than 10 so a(10000) = 255558 (the concatenation of these factors in nondecreasing order). - _David A. Corneth_, Jul 31 2017
%t A068189 f[x_] := Apply[Times, IntegerDigits[x]] a = Table[0, {256} ]; Do[ b = f[n]; If[b < 257 && a[[b]] == 0, a[[b]] =n], {n, 1, 10000} ]; a
%o A068189 (PARI) a(n) = {if(n==1, return(1)); my(res = []); forstep(i=9,2,-1, v = valuation(n, i); if(v > 0, res = concat(vector(v, j, i), res); n/=i^v)); if(n==1,fromdigits(res), 0)} \\ _David A. Corneth_, Jul 31 2017
%o A068189 (Python)
%o A068189 def convert(n):
%o A068189     if n == 1:
%o A068189         return 1
%o A068189     result = 0
%o A068189     cur = 1
%o A068189     while n > 1:
%o A068189         found = False
%o A068189         for i in range(9, 1, -1):
%o A068189             if n % i == 0:
%o A068189                 result += cur * i
%o A068189                 cur *= 10
%o A068189                 n //= i
%o A068189                 found = True
%o A068189                 break
%o A068189         if not found:
%o A068189             return 0
%o A068189     return result
%o A068189 N = 256
%o A068189 for n in range(1, N):
%o A068189     print(n, convert(n))
%o A068189 # _Dmitry Kamenetsky_, Oct 20 2008
%Y A068189 Cf. A001222, A002473, A007954, A067734, A068183-A068187, A068189-A068191.
%Y A068189 Cf. A085123, A280249.
%K A068189 base,nonn
%O A068189 1,2
%A A068189 _Labos Elemer_, Feb 19 2002