[seqfan] Sequence like A026272 but uses 3 integers instead of 2.

[DAN_CYN_J]

Hi again seq. fans, 

Can this sequence continue --->oo ? 


A complex sequence where all integers are represented just 3 times, 
The problem arises when two integers need to share the same index. 
In that case the smaller integer wins out and the gap that represents 
that larger integer is increased by (1) for that entry and the 
same gap for the next entry. 

In the sequence below (1) can be repeated (3) times with a (1) gap because it has 
precedent over (2). 

(2) gap therefore has to be increased by (1) for that 
entry and the same gap for the next entry. if another conflict arises 
then the one with no change in its gap adds one more to its gap size. 
In other words no gap can exceed it integer equivalent >1. 

(14) is and example below where it starts with a gap of (14) but has to change 
the gap to (15) because (18) already has a (19) gap assigned to it. 



A similar sequence that produces each integer (twice) instead of 3 times 
is in OEIS as A026272 


Is an algorithm with the above rules to create this sequence possible? 


I believe there is but I lack the sophistication to create one. 



I do believe this to be correct for the first 3/4 of the terms! 
(remember the latter terms always need adjusting as each integer set is completed) 

(n) = completed integer represented 3 times. 
  
1,2,1,3,(1),2,4,3,5,(2),6,(3),4,7,5,8,9,6,(4),10,(5),7,11,12,(6),8,9,13,14,(7),10,15,16,17,11,(8),(9),12,18,19,20,(10),13,14,21,22,(11),15,23,16,24,(12),17,25,26,27,28,(13),18,(14),19,20,29,(15),30,31,(16),21,22,32,33,(17),23,34,35,24,36,37,(18),25,38,(19),26,(20),27,28,39,40,41,42,(21),(22),29,43.44,30,(23),31,45,46,(24),47,32,48,33,(25),49,50,34,51,(26),35,52,(27),36,(28),53,54,55,56,57,58,(29),59,60,61,(30),62,63,(31),64,65,66,67,68,(32),69,70,(33),71,72,73,74,(34),75,76,77,78,(35),79,80,81,(36),... --->00?? 

  

This sequence has to be continually adjusted for at least the last 1/4 of the terms. 
So the latter part of this sequence contain the wrong first integer added 
which will ultimately be less for that particular index. 
  
(*) where (1) is added to the gap of certain integers and continues with the same gap for 
the last integer. 

1=1 gap 
2=3 gap * 
3=3 gap 
4=5 gap * 
5=5 gap 
6=6 gap 
7=7 gap 
8=9 gap * 
9=9 gap 
10=10 gap 
11=11 gap 
12=13 gap * 
13=14 gap * 
14=14 gap and between the 2nd (14) and 3rd (14) 14= a 15 gap * 
15=15 gap 
16=16 gap 
17=18 gap * 
18=19 gap * 
19=20 gap * 
20=20 gap  and between the 2nd (20) and 3rd (20) 20= a 21 gap * 
21=22 gap * 
22=22 gap 
23=23 gap 
24=24 gap 
25=25 gap 
26=27 gap * 
27=28 gap * 
28=28 gap and between the 2nd (28) and 3rd (28) 28= a 29 gap * 
29=29 gap 
30=30 gap 
31=31 gap 
32=32 gap 
33=33 gap 
34=34 gap 
35=36 gap * 
36=37 gap * 
... 
I hope there are no errors up to 3/4 the way threw this sequence because 

that would screw up the whole sequence. 


This was all done by brute force so any errors are possible! 

  

Cheers, 

  

Dan