[seqfan] Re: A new sequence?

[DAN_CYN_J]

Hi again seq. fans, 

  

Here is the next sequence using only all positive odd integers that represents all odd 
integers just twice. 


Their gap count also equals the odd integer. 

  

1,3,1,5,7,3,9,11,13,5,15,17,7,19,21,23,9,25,27,11,29,31,13,33,35,37,15,39,41,17,43,45,47,19, 
49,51,21,53,55,23,57,59,61,25,63,65,27,67,69,71,29,73,75,31,77,79,81,33,83,85,35,87,89,37, 
91,93,95,39,97,99,41,101,103,105,43,107,109,45,111,113,47,115,117,119,49,121,123,51,125,127, 
129,53,131,133,55,135,137,139,57,141,143,59,145,147,61,149,151,153,63,155,157,65,159,161,163, 
67,165,167,69,169,171,71,173,175,177,73,179,181,75,183,185,187,77,189,191,79,193,195,81,197, 
199,201,83,203,205,85,207,209,211,87,213,215,89,217,219,221,91,223,225,93,227,229,95,231,233, 
235,97,237,239,99,241,243,245,101,247,249,103,251,253,105,255,257,259,107,261,263,109,265,267, 
269,111,271,273,113,275,277,279,115,281,283,117,285,287,119,289,291,293,121,295,297,123,299,  
301,303,125,305,307,127,309,311,129,313,315,317,131,... 

  

It appears to be converging very slowly also too the silver mean ~ 2.41535... 

  

Dan 

------------------------------------------------------------------------------------------------------------------------------------------------- 
From: "DAN_CYN_J" <dan_cyn_j at comcast.net> 
To: "." <seqfan at list.seqfan.eu> 
Sent: Sunday, April 7, 2013 9:50:13 PM 
Subject: [seqfan] A new sequence? 

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. 

  

2,4,6,2,8,10,4,12,14,6,16,18,20,8,22,24,10,26,28,30,12,32,34,14,36,38,40,16,42,44,18, 
46,48,20,50,52,54,22,56,58,24,... 

It is related to the silver mean whose cf = [2:2,2,2,2,2,2,2,2,2,2,2,...] 
= 
2.4142135623730950488016887242096980785696718753769480731766797379907324784... 

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...] ? 

  

Dan  

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