# [seqfan] a(n) is the a(n)th absolute first difference of S

Eric Angelini Eric.Angelini at kntv.be
Fri Nov 26 10:41:18 CET 2010

```Hello Seqfans,

Here is a kind of self-describing sequence S,
where a(n) is the a(n)th absolute first difference of S.

n = 1 2 3 4 5  6 7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
a(n) = 1,2,4,5,9,14,8,10,18,27,17, 6,11,15,29,44,19,36,54,35,21,42,23,46,25,50,28,55,...
diff =  1 2 1 4 5  6 2  8  9  10 11 5  4  14 15 25 17 18 19 14 21 19 23 21 25 22
d-rank= 1 2 3 4 5  6 7  8  9  10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
hit:    * *   * *  *    *  *   *  *     *  *  *     *  *  *     *     *     *

S is tricky to compute; the rule for a(n+1) is "always
use the smallest integer not yet in S and not leading to

Example:

'14' is in S and '14' says: "The 14th absolute first
difference in S equals 14" -- which is true.

The Recaman sequence is also self-describing in the way
meant here -- but A005132 comes lexicographically after
this one : http://oeis.org/A005132 (and you have to drop
the initial "0"):

If we want S to be monotonically increasing we get A063733:

http://oeis.org/A063733

If this is of interest, could someone compute a hundred
terms or so and submit?

Best,
É.

```