[seqfan] Fractions, digits, decimal expansion

[Eric Angelini]

Hello SeqFans, 
Here is an echo to the seq computed by Hans Havermann last July:
https://oeis.org/A257664

a(1)=1; a(n+1) is the smallest positive integer not yet used 
such that the set of the different digits present in the 
fraction F=a(n)/a(n+1) is visible in the decimal expansion of F:

S = 1,6,13,10,14,17,7,8,...

Example:
1/6 = 0,1666... (we see 1 and 6)
6/13 = 0,461538461538... (we see 6, 1 and 3)
13/10 = 1,30 (yes, we admit this zero)
10/14 = 0,7142857142... (we see 1, 0 and 4)
14/17 = 0,8235294117... (we see 1, 4 and 7)
17/7 = 2,4285714285... (we see 1 and 7)
7/8 = 0,875 (we see 7 and 8)
etc.

Is S a permutation of the natural numbers > 0?

Best,
É.