A217618 - OEIS

%I #10 Dec 28 2022 05:43:48

%S 3,2,3,2,3,4,5,3,11,2,3,2,3,2,5,3,3,16,3,2,15,2,5,2,3,8,5,3,11,2,3,2,

%T 3,2,5,8,3,6,3,2,13,2,13,2,3,10,11,5,11,4,3,4,3,9,13,4,3,7,3,4,13,4,5,

%U 7,3,4,5,3,11,4,5,4,7,3,5,3,7,6,5,3,17,3

%N a(n) = A217578(n)/n.

%C Inspired by Problem 300 in Mathematical Excalibur, Vol. 13, No. 1, February-April, 2008.

%H Michel Marcus, <a href="/A217618/b217618.txt">Table of n, a(n) for n = 1..1000</a>

%H Kin Y. Li, <a href="http://www.math.ust.hk/excalibur/v13_n1.pdf">Problem 300</a>, Mathematical Excalibur, Vol. 13, No. 1, February-April, 2008.

%e For n=5, odd, 5*2=10, 5*3=15, so 3 is the smallest k such that all digits of 5*k are odd.

%e For n=8, even, 8*2=16, 8*3=24, so 3 is the smallest k such that all digits of 8*k are even.

%t Table[k = 2; While[d = IntegerDigits[k*n]; If[OddQ[n], done = And @@ OddQ[d], done = And @@ EvenQ[d]]; ! done, k++]; k, {n, 100}] (* _T. D. Noe_, Oct 10 2012 *)

%Y Cf. A217578.

%K nonn,base

%O 1,1

%A _Michel Marcus_, Oct 09 2012