[seqfan] Pi digits shuffled with negative terms

[Eric Angelini]

Hello SeqFans,
Here is a proposition for a new sequence S:

S = 9,3,4,5,1,1,8,5,9,5,3,9,7,-1,8,3,2,3,4,6,6,8,2,4,3,3,9,7,3,-1,-1,2,5,8,8,2,0,9,4,7,-1,6,1,9,1,9,9,3,-1,-1,7,-1,3,5,8,5,1,9,0,2,7,9,0,4,-1,9,4,4,5,7,3,2,0,...

To recover Pi's decimals, just obey the hereunder rules:
(a) underline all negative terms of S;
(b) pick always "d", the leftmost not underlined term, jump
    over "d" terms to the right and underline "d";
(c) goto instruction(b)
(d) at the end of the process, discard the negative terms.

Example (an underlined term is followed by a star):

Start:  S=9,3,4,5,1,1,8,5,9,5,3,9,7,-1,8,3,2, ...
step(a) S=9,3,4,5,1,1,8,5,9,5,3,9,7,-1*,8,3,2, ...
step(b) S=.,3,4,5,1,1,8,5,9,5,9*,3,9,7,-1*,8,3,2, ...
   (b) S=.,.,4,5,1,3*,1,8,5,9,5,9*,3,9,7,-1*,8,3,2, ...
   (b) S=.,.,.,5,1,3*,1,4*,8,5,9,5,9*,3,9,7,-1*,8,3,2, ...
   (b) S=.,.,.,.,1,3*,1,4*,8,5*,5,9,5,9*,3,9,7,-1*,8,3,2, ...
   (b) S=.,.,.,.,.,3*,1*,1,4*,8,5*,5,9,5,9*,3,9,7,-1*,8,3,2, ...
   (b) S=.,.,.,.,.,3*,1*,.,4*,1*,8,5*,5,9,5,9*,3,9,7,-1*,8,3,2, ...
   (b) S=.,.,.,.,.,3*,1*,.,4*,1*,.,5*,5,9,5,9*,3,9,7,8*,-1*,8,3,2, ...
   (b) S=.,.,.,.,.,3*,1*,.,4*,1*,.,5*,.,9,5,9*,3,9,5*,7,8*,-1*,8,3,2, ...
   (b) S=.,.,.,.,.,3*,1*,.,4*,1*,.,5*,.,.,5,9*,3,9,5*,7,8*,-1*,8,9*,3,2, ...
   (b) S=.,.,.,.,.,3*,1*,.,4*,1*,.,5*,.,.,.,9*,3,9,5*,7,5*,8*,-1*,8,9*,3,2, ...
   (b) S=.,.,.,.,.,3*,1*,.,4*,1*,.,5*,.,.,.,9*,.,9,5*,7,3*,5*,8*,-1*,8,9*,3,2, ...
   (b) S=.,.,.,.,.,3*,1*,.,4*,1*,.,5*,.,.,.,9*,.,.,5*,7,3*,5*,8*,-1*,8,9*,3,9*,2, ...
   (b) S=.,.,.,.,.,3*,1*,.,4*,1*,.,5*,.,.,.,9*,.,.,5*,.,3*,5*,8*,-1*,8,9*,3,7*,9*,2, ...
   (b) S=.,.,.,.,.,3*,1*,.,4*,1*,.,5*,.,.,.,9*,.,.,5*,.,3*,5*,8*,-1*,.,9*,3,7*,9*,2, ...
step(d) S=          3  1    4  1    5        9      5    3  5  8        9    7  9     ...
END --> we see Pi's decimals appearing.

Question:
The above shuffle might not be optimal (in terms of negative
terms quantity): is it possible to improve?
Best,
É.