First digits after the decimal point

(Dall-e creation)

If a, b and c are three successive terms of a sequence S, we want that a is what we see immediately after the decimal point when b is divided by c (we do not take into account the leading zeros between the decimal point and a). 

I guess S could start like this (S being the lexico-earliest sequence of distinct positive terms):

S = 1,2,11,5,42,4,94,38,401,1029,2560,...

1 is what we see after the decimal point when 2 is divided by 11 (indeed 2/11 = 0.18181818181...)

2 is what we see after the decimal point when 11 is divided by 5 (indeed 11/5 = 2.2)

11 is what we see after the decimal point when 5 is divided by 42 (indeed 5/42 = 0.11904761904...)

5 is what we see after the decimal point when 42 is divided by 4 (indeed 42/4 = 10.5)

42 is what we see after the decimal point when 4 is divided by 94 (indeed 4/94 = 0.04255319148...)

4 is what we see after the decimal point when 94 is divided by 38 (indeed 94/38 = 2.47368421053...)

94 is what we see after the decimal point when 38 is divided by 401 (indeed 38/401 = 0.09476309226...)

38 is what we see after the decimal point when 401 is divided by 1029 (indeed 401/1029 = 0.38969873663...)

401 is what we see after the decimal point when 1029 is divided by 2560 (indeed 1029/2560 = 0.401953125)

etc.

____________________

December 31st, 2023, update

Hans Havermann was quick to spot a lexico-earlier seq:

ÉA

> S = 1, 2, 11, 5, 42, 4, 94, 38, ...

> 4 is what we see after the decimal point when 94 is divided by 38 (indeed 94/38 = 2.47368421053...)

HH ... But 4 is also what we see after the decimal point when 94 is divided by 7 (indeed 94/7 = 13.42857142857...) and 7 < 38, so:

S = 1, 2, 11, 5, 42, 4, 94, 7, ...

ÉA

Many thanks for the correction, Hans — and a happy new 2024 for you!

(Dalle-e creation)