# [seqfan] Three infinite sequences

David Corneth davidacorneth at gmail.com
Sat May 30 17:30:55 CEST 2015

```Hi All,

I think the way to go for S is to look at partitions of 1 though 9.
For example, partitions of 3 are
3, 2 + 1, 1 + 1 + 1
This means that all positive integers containing only
3,3 and all others 0 or
3,2,1 and all others 0 or
3,1,1,1 and all others 0 are in P.
All elements of P can be constructed as such. This enables finding or just
counting without listing
all elements below 10^n for some n (which might be another sequence).

A Similar but slightly changed thing can be done for P;
factorizations of 8 with integer factors > 1 are 2^3, 2 * 4, 8
This means that all positive integers containing only
8,2,2,2 and all others 1 or
8,4,2 and all others 1 or
8, 8 and all others 1 or
two zero's and the other digits whatever you like.
This way again enables finding or just counting without listing
all elements below 10^n for some n (which might be another sequence).

Similar again for INT.

Best regards,
David
```