[seqfan] Re: A new sequence?

DAN_CYN_J dan_cyn_j at comcast.net
Mon Apr 8 15:40:30 CEST 2013



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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