Second _absolute_ differences

[Eric Angelini]

... 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?
 
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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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