[seqfan] a(n) ends like the sum of the first n terms of U

[Eric Angelini]

Hello SeqFans,
I think U is not in the OEIS - and if so, I would need a little
help in computing it.

U is the lexically first sequence having no term repeated such
that a(n) ends like the sum of the first n terms of U.

U = 1,3,9,5,7,8,14,11,21,12,20,101,15,87,16,86,18,84,22,80,201,301,...

U was extended using always the smallest integer not yet present
in U and not leading to a contradiction.

We see here that:

1 ends like the sum 1
3 ends like the sum of the first 3 terms [1+3+9=13]
9 ends like the sum of the first 9 terms [1+3+9+5+7+8+14+11+21=79]
5 ends like the sum of the first 5 terms [1+3+9+5+7=25]
7 ends like the sum of the first 7 terms [1+3+9+5+7+8+14=47]
8 ends like the sum of the first 8 terms [1+3+9+5+7+8+14+11=58]
etc.

Let's use S for the cumulative sum of U's terms and n for n:

U= 1,3, 9, 5, 7, 8,14,11,21,12, 20,101, 15, 87, 16, 86, 18, 84, 22,...
S= 1,4,13,18,25,33,47,58,79,91,111,212,227,314,330,416,434,518,540,...
n= 1 2  3  4  5  6  7  8  9 10  11  12  13  14  15  16  17  18  19 ...
     -     -     -          --          --      --      --      --
When n doesn't end like S(n), we have a term not in U (underlined).

Best again,
É.