A174813 - OEIS

%I #22 Jun 28 2025 09:52:44

%S 1,3,9,11,13,19,31,33,39,91,93,99,111,113,119,131,133,139,191,193,199,

%T 311,313,319,331,333,339,391,393,399,911,913,919,931,933,939,991,993,

%U 999,1111,1113,1119,1131,1133,1139,1191,1193,1199,1311,1313,1319,1331

%N a(n) = number whose product of digits equals a power of 3.

%C Equivalently, numbers whose decimal representation consists of digits from the set {1,3,9}.

%H Reinhard Zumkeller, <a href="/A174813/b174813.txt">Table of n, a(n) for n = 1..10000</a>

%e a(9)=39 is in the sequence because 3*9=3^3.

%t Select[Range[2000], IntegerQ[Log[3, Times @@ (IntegerDigits[#])]] &]

%o (Haskell)

%o a174813 n = a174813_list !! (n-1)

%o a174813_list = f [1] where

%o    f ds = foldr (\d v -> 10 * v + d) 0 ds : f (s ds)

%o    s [] = [1]; s (9:ds) = 1 : s ds; s (d:ds) = 3*d : ds

%o -- _Reinhard Zumkeller_, Jan 13 2014

%o (Python)

%o from sympy import integer_log

%o def A174813(n):

%o     m = integer_log(k:=(n<<1)+1,3)[0]

%o     return sum(3**((k-3**m)//(3**j<<1)%3)*10**j for j in range(m)) # _Chai Wah Wu_, Jun 28 2025

%Y Cf. A028846, A061427.

%K nonn,base

%O 1,2

%A _Michel Lagneau_, Dec 01 2010