[seqfan] Re: Nx and N+ triangles

[M. F. Hasler]

On Fri, Jun 24, 2016 at 6:43 AM, Zak Seidov <seqfan at list.seqfan.eu> wrote:
> 7
> 49
> 2863
> 14564221
> 72835422814147
> 49145621352814145672872849

This is A061585 : multiply by 7 each digit

> 7
> 14
> 811
> 1588
> 8121515
> 1589812815
> 81215161589812

This is A061522 : add 7 to each digit

The others follow the same pattern.
Maybe not all are in OEIS...

Some seem to converge to a "fixed point" for the substitution (seen as
an infinite chain of digits, not as one number, of course).
For some others, it might be that there is k such that each
subsequence of every k-th term does converge in that sense;
e.g. for the Nx[7] operator, k=4,
a({1,5,9,...}) -> 7283542281....,
a({2,6,10,...}) -> 4914562135....
a({3,7,11,...}) -> 286372835...
a({4,8,12,...}) -> 14564221491...

For the N+[7] operator, k=2 and the two limits are
158981281...  and  81215161589...
Maybe (some)one can prove that this is always the case?

M.