[seqfan] To reach the next "1"

[Eric Angelini]

Hello SeqFans,

S = 2,0,1,10,12,3,4,5,6,7,8,9,20,13,22,23,
24,25,26,21,27,31,28,29,14,30,32,15,
33,34,41,35,36,37,51,38,39,40,42,16,
43,44,45,46,17,47,48,49,50,52,...

The quantity of digits necessary to reach
the next "1" is given by the sequence itself --
which was always extended with
the smallest integer not yet present in S
and not leading to a contradiction.

Example:
There are 2 digits between the start and the "1" of 1;
There are 0 digits between 1 and the "1" of 10;
There is 1 digit between the "1" of 10
and the "1" of 12;
There are 10 digits between the "1" of 12
and the "1" of 13;
etc.
S is not a permutation of the non-negative
integers ("11" will never show, for instance).

Best,
É.
(9 more sequences of this type are
possible with the 9 other digit-markers)