# [seqfan] Add the remainder -- divide by the next digit

Eric Angelini Eric.Angelini at kntv.be
Mon Mar 12 15:22:33 CET 2012

```Hello Seqfans,

Start the sequence S with a(1)
- divide a(1) by the 1st digit of S
- add the remainder to a(1) to get a(2)
- divide a(2) by the 2nd digit of S
- add the remainder to a(2) to get a(3)
- divide a(3) by the 3rd digit of S
- add the remainder to a(3) to get a(4)
- divide a(4) by the 4th digit of S

Never divide by 0 -- divide by 10 instead.

Example with a(1) = 13:
S = 13
S = 13, 13
S = 13, 13, 14
S = 13, 13, 14, 14
S = 13, 13, 14, 14, 16,
S = 13, 13, 14, 14, 16, 16,
S = 13, 13, 14, 14, 16, 16, 16
S = 13, 13, 14, 14, 16, 16, 16, 16,
S = 13, 13, 14, 14, 16, 16, 16, 16, 16,
S = 13, 13, 14, 14, 16, 16, 16, 16, 16, 16,
S = 13, 13, 14, 14, 16, 16, 16, 16, 16, 16, 20,
S = 13, 13, 14, 14, 16, 16, 16, 16, 16, 16, 20, 20,
S = 13, 13, 14, 14, 16, 16, 16, 16, 16, 16, 20, 20, 22,
S = 13, 13, 14, 14, 16, 16, 16, 16, 16, 16, 20, 20, 22, 22,
S = 13, 13, 14, 14, 16, 16, 16, 16, 16, 16, 20, 20, 22, 22, 26,
S = 13, 13, 14, 14, 16, 16, 16, 16, 16, 16, 20, 20, 22, 22, 26, 26,
S = 13, 13, 14, 14, 16, 16, 16, 16, 16, 16, 20, 20, 22, 22, 26, 26, 28,
S = 13, 13, 14, 14, 16, 16, 16, 16, 16, 16, 20, 20, 22, 22, 26, 26, 28, 28,
S = 13, 13, 14, 14, 16, 16, 16, 16, 16, 16, 20, 20, 22, 22, 26, 26, 28, 28, 32,
S = 13, 13, 14, 14, 16, 16, 16, 16, 16, 16, 20, 20, 22, 22, 26, 26, 28, 28, 32, 32,
S = 13, 13, 14, 14, 16, 16, 16, 16, 16, 16, 20, 20, 22, 22, 26, 26, 28, 28, 32, 32, 34, ...

Do all integers end on a fixed point?
Best,
É.

```