# [seqfan] A seed and a jumping bean

Eric Angelini Eric.Angelini at kntv.be
Fri Oct 7 12:34:33 CEST 2011

```Hello SeqFans,
sorry to post only a link and a couple of lines,
but S is quite complex to explain in ASCII format
:-(
Best,
É.

Consider S:
S=0,1,1,1,2,3,1,3,6,3,1,5,10,7,1,3,14,7,1,13,18,7,1,3,22,11,1,21,26,15,1,3,30,7,1,29,34,15,1,3,38,27,1,37,42,
n=1,2,3,4,5,6,7,8,9,1,1,1, 1,1,1,1, 1,1,1, 2, 2,2,2,2, 2, 2,2, 2, 2, 3,3,3, 3,3,3, 3, 3, 3,3,4, 4, 4,4, 4, 4,
0 1 2  3 4 5 6  7 8 9  0  1 2 3 4  5  6 7  8  9  0 1 2  3 4 5  6  7  8 9 0  1  2 3  4  5
[Read "n" vertically; thus S(10)=3, S(25)=22 and S(47)=1, for instance.]

S works like this:
- take any S(n), the "seed" --> for instance, for n=10, take S(10)=3 (this 3 is "the seed");
- jump from S(n) to the right over S(n) integers --> from S(10)=3 over 1,5,10 (3 integers);
- land on S[n+1+S(n)], "the bean" --> land on 7, "the bean";
S has been build in order to always have S(n)+S[n+1+S(n)]=n (or "seed"+"bean"=n --> 3+7=10).

This sequence is infinite and well defined.

(...)

```