[seqfan] pan-Belgian numbers

[Giovanni Resta]

Today I've stumbled upon k-Belgian numbers
( https://oeis.org/A106039 ) defined by Eric Angelini.

I noticed that trivially all the numbers n >= 10
and made of zeros and ones only, are pan-Belgian, i.e.,
they are k-Belgian for k=0,1,...,9.

I searched for pan-Belgian numbers not entirely made
of 0 and 1.

The smallest I found are (if I'm correct)
1111111113, 1111111114, 1111111115, 1111111118, 1111111119,
1111111411, 1111116111, 1113111111, 1211111111, 8111111111,
10111111113, 10111111119, 10111116111, 10111151111, 10112111111,
10113111111, 11011111113, 11011111119, 11011116111, 11013111111, ...

The 1000-th such number (where I stopped my search) is
111793111111 and among these 1000 I did not find any
with more than 3 digits different from 0 and 1.

I doubt this sequence is worth submitting, but I thought
it is curious enough (at least for Eric, I hope... ) to be
cited here.

giovanni