cp's OEIS Frontend

A068187 a(n) is the smallest number such that the product of its decimal digits equals n^n, or 0 if no solutions exist.

%I A068187 #22 Aug 14 2017 03:26:22
%S A068187 1,4,39,488,55555,88999,7777777,88888888,999999999,25555555555888,0,
%T A068187 88888888999999,0,4777777777777778888,35555555555555559999999,
%U A068187 2888888888888888888888,0,888888999999999999999999,0,2555555555555555555558888888888888,37777777777777777777779999999999
%N A068187 a(n) is the smallest number such that the product of its decimal digits equals n^n, or 0 if no solutions exist.
%C A068187 a(n) = 0 if and only if n has a prime factor > 7. If n > 1 has no prime factor > 7, let n^n = 2^a*3^b*5^c*7^d. Let m(x) denote the number of digit x in a(n). Then a(n) is a number whose digits are nondecreasing and defined as follows. m(2) = 1 if a mod 3 == 1 and 0 otherwise, m(3) = 1 if b mod 2 == 1 and 0 otherwise, m(4) = 1 if a mod 3 == 2 and 0 otherwise, m(5) = c, m(6) = 0, m(7) = d, m(8) = floor(a/3), m(9) = floor(b/2). - _Chai Wah Wu_, Aug 12 2017
%H A068187 Chai Wah Wu, <a href="/A068187/b068187.txt">Table of n, a(n) for n = 1..200</a>
%o A068187 (Python)
%o A068187 from sympy import factorint
%o A068187 def A068187(n):
%o A068187     if n == 1:
%o A068187         return 1
%o A068187     pf = factorint(n)
%o A068187     return 0 if max(pf) > 7 else int(''.join(sorted(''.join(str(a)*(n*b) for a,b in pf.items()).replace('222','8').replace('22','4').replace('33','9')))) # _Chai Wah Wu_, Aug 13 2017
%Y A068187 Cf. A000312, A067734, A068183, A068184, A068185, A068186, A068188, A068190.
%K A068187 base,nonn
%O A068187 1,2
%A A068187 _Labos Elemer_, Feb 18 2002
%E A068187 Edited by _Dean Hickerson_ and _Henry Bottomley_, Mar 07 2002