[seqfan] Runs of digits of size a(n)

[Eric Angelini]

Hello SeqFans,

Runs of digits of size a(n), which start with a(n) and sum up to a(n):

R = 1,10,11,12,20,110,111,112,13,21,100,101,13,15,16,17,18,19,22,23,24,25,26,27,30,102,a,...
(a is 10^51)

Example:
10 is the sum of the 10 digit-run which starts with 10:
[1,0,1,1,1,2,2,0,1,1]

11 is the sum of the 11 digit-run which starts with 11:
[1,1,1,2,2,0,1,1,0,1,1]

12 is the sum of the 12 digit-run which starts with 12:
[1,2,2,0,1,1,0,1,1,1,1,1]

20 is the sum of the 20 digit-run which starts with 20:
[2,0,1,1,0,1,1,1,1,1,2,1,3,2,1,1,0,0,1,0]

etc. In extending R, always try to use the smallest available integer not present in R and not leading to a contradiction.

Best,
É.