RE : Second _absolute_ differences

[Eric Angelini]

Eric (me) wrote:
> 1 1 1 1 2 2 2 2 4 4 4 4 8 8 8 8 16 16 16 16 32 32 32 32 64 64 64 64 ... 
> I'm looking for less trivial ones...
 
I've just found this seq. (among others) which is equal to it's fourth
absolute diff.:
 
7 1 5 3 14 2 10 6 28 4 20 12 56 8 40 24 112 16 80 48 224 32 160 96 448 ..
 
The similar seq. below (first terms in different order) enters in another
4th-absolute-diff sequence:
 
1 3 5 7 2 6 10 14 4 12 20 28 8 24 40 56 16 48 80 112 32 96 160 224 64 ...
enters in:
3 1 1 1 6 2 2 2 12 4 4 4 24 8 8 8 48 16 16 16 96 32 32 32 192 64 64 64 ...
which loops.
 
Best,
E.

________________________________

De: Eric Angelini
Date: dim. 07/01/2007 23:16
À: seqfan at ext.jussieu.fr
Cc: alexandre.wajnberg at skynet.be
Objet : Second _absolute_ differences


 
... of this sequence, are the sequence itself:
 
1,3,2,6,4,12,8,24,16,48,32,96,64,192,128,384,256,768,512,1536,1024,3072, ...
 
This is always true if you interleave sequences (1) and (2) like that:
 
(1) a  2a  4a  8a  16a  32a  64a  128a ...
(2)   b  2b  4b  8b  16b  32b  64b   128b ...
 
Above, we have a=1 and b=3
 
The sequence is a mix of A000079:
1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,
 
and A007283:
3,6,12,24,48,96, 192,384,768,1536,3072,6144,12288,
 
... which are both their own first differences.
 
Is this old hat?
 
----------------
 
The sequence below is it's own |fourth absolute differences| :
 
1 1 1 1 2 2 2 2 4 4 4 4 8 8 8 8 16 16 16 16 32 32 32 32 64 64 64 64 ...
 
I'm looking for less trivial ones...
Best,
E.
 
 
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