%I #5 Dec 15 2015 14:44:50

%S 1,6,13,17,7,8,14,19,23,21,29,34,31,3,38,28,46,47,35,39,49,43,51,42,

%T 41,48,53,26,12,57,58,59,2,61,24,68,11,52,63,22,69,62,71,56,65,76,81,

%U 44,67,64,83,85,78,77,79,72,70,87,80,89,9,86,92,73,27,84,93

%N a(1)=1; a(n+1) is the smallest positive integer not yet used where all the digits of a(n) and a(n+1) are present in the decimal expansion (excluding any leading or trailing zeros) of a(n)/a(n+1).

%C Conjecture: a(n) is a permutation of the natural numbers.

%H Hans Havermann, <a href="/A265756/b265756.txt">Table of n, a(n) for n = 1..10000</a>

%e 1/6 = .1666... (1 and 6)

%e 6/13 = .461538461538... (1, 3 and 6)

%e 13/17 = .76470588235294117647058823529411... (1,3 and 7)

%e Note that term 4 is not 10 because 13/10 = 1.3 (no zero)

%t t=1; s={1}; Do[c=1; d=IntegerDigits[t]; While[f=Flatten[RealDigits[t/c][[1]]]; u=Union[IntegerDigits[c], d]; Union[Table[MemberQ[f, u[[i]]], {i, Length[u]}]]!={True}||MemberQ[s, c], c++]; t=c; AppendTo[s, t], {400}]; s

%Y Cf. A257664, A265740.

%K nonn,base

%O 1,2

%A _Hans Havermann_, Dec 15 2015