[seqfan] Nice kind of A030067

[Eric Angelini]

Hello SeqFans,

The "semi-Fibonacci numbers" are there:
http://www.research.att.com/~njas/sequences/A030067

If you drop the increasing constraint (of the odd rank
terms) you'll get S:

S=1,1,2,1,1,2,3,1,2,1,1,2,3,3,6,1,5,2,3,1,2,1,1,2,3,3,6,3,3,6,9,1,8,5,3,2,...

Which is kind of selfdescribing:

"The succession of the absolute differences between 
odd rank terms is the sequence itself"

In other words: underline all terms of odd rank in S;
these rebuild S itself; an underlined term is the ab-
solute difference of its two immediate neighbours.

The sequence will show every integer.

S was build with the interdiction of having a zero. If
you allow zero in S you'll get T, which is rather dull:

T=1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,...

Best,
É.