April 17th, 2017, 01:15 PM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 397 Thanks: 27 Math Focus: Number theory  Seeking the sequence
Without looking at OEIS, what is the significance of the following fundamental yet overlooked sequence? 0, 1, 1, 1, 2, 2, 4, 8, 12, 96... 
April 18th, 2017, 09:57 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,367 Thanks: 1272 
it looks like $a_0=0$ $a_1=1$ $a_{2k} = a_{2k1}+a_{2k2}$ $a_{2k+1} = a_{2k} \cdot a_{2k1}$ significance of it? No idea. 
April 18th, 2017, 10:07 AM  #3 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 397 Thanks: 27 Math Focus: Number theory 
The significance is simplicity and you got it!

April 18th, 2017, 12:56 PM  #4 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,616 Thanks: 2605 Math Focus: Mainly analysis and algebra 
I don't know why you'd call it fundamental.

April 18th, 2017, 02:03 PM  #5 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 397 Thanks: 27 Math Focus: Number theory 
Starting on zero and one, two fundamentally related operations alternate. OEIS reveals these numbers eventually as 2^Fibonacci(n3). 

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