April 17th, 2017, 01:15 PM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 270 Thanks: 23 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: Southern California, USA Posts: 1,497 Thanks: 755 
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: 270 Thanks: 23 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: 6,973 Thanks: 2295 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: 270 Thanks: 23 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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