[seqfan] A new sequence?

DAN_CYN_J dan_cyn_j at comcast.net
Mon Apr 8 03:50:13 CEST 2013

Hi all sequence fans, 


A nice new sequence related to A026272. 


A sequence where all even positive integers are represented exactly twice. 
Also the even gap count between the integer represent that integer. 



It is related to the silver mean whose cf = [2:2,2,2,2,2,2,2,2,2,2,2,...] 

When a(n) value is < a(n-1) then a(n-1)/a(n) will converge too the silver mean. 


Just like A026272 --- 1,2,1,3,2,4,5,3,6,7,4,8,5... sequence where certain 
consecutive integers converges too phi where the best phi convergence happens 
at the Fibonacci pairs within the sequence.  [3,2],[5,3],[8,5],[13,8]... 


I am not sure other sequences can be produced related to this same format 
to converge on the next larger metal mean such as cf =[3:3,3,3,3,3,3,3...] ? 



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