6 years, 75 days

## Convergent subsequences...

Thanks for this. I am interested in what you say but cannot see the subsequences of a(n)/n that you refer to. How did you find them?

Do you have any further details so I can take a look at it? I'm guessing each subsequence is of the form a(f(n))/f(n) for some simple function f of n.. ?

## Plots...

Thank you, works perfectly, very useful plots don't know why it didn't work at first but all ok now. My version is 2017.
How do I do a thumbs up to show my appreciation for this assistance?

## Plots etc....

The plots now work fine now, and that one-off "break" at a(229)=6 is interesting. At that point the odd terms resolve from one into two parallel lines, and the line of even terms (at which the "break" occurs) restarts at a(229), at first producing multiples of 6 until after a(337) = 168. Since no further breaks seem to occur further out it looks like we see no more than 28 multiples of 6. Hence likely that sequence is not a permutation.

Thank you very much for your help with this.

## Sequence/plot...

Hi,

Thanks for the suggestion, I tried it but without success; got plot coordinates but not the graph.
Anything else I can try?

## Sequence plot...

Hi,

Thanks for your suggestion but I cannot get it to work. I get a list of tbe graph coordinates but not the graph itself; any suggestions? Ideally I would like to see both pin plot and log log plot

## Sequence/quibbles....

Agreed, thank you. Am still unable to get a graph, having tried both proposed methods.

## Heap etc....

@Carl Love Thank you very much, nice solution, it works perfectly (I thought you might like to tackle the "tricky" bit). Could you say how to graph it? The data suggests ta(n) <= n;  is there a way to check this up to some arbitrary N? Likewise can we check a(n)+a(n+1) <= n +1 ? (I guess the first always holds, but maybe not the second...).

## Another error message...

@Carl Love Graph with separation of provenance of terms is indeed interesting.

I got this when tried to run the above code :

"Error, invalid left hand side of multiple assignment"

Any suggestions?

## lost the plot...

@Carl LoveTried your suggestion, got this:

"Error, listplots is not a command in the plots package"

Could you write is out exactly for me please?

ps: the inequality bit worked fine

## Thanks...

@Kitonum Thank you , all went well, see question above for TomLeslie, woud be interesting to analyse plot a bit,

## Thanks...

@tomleslie Thank you, it works fine, interesting graph. Is there a way to highlight the points on the graph associated with each of the two generating rules, eg if a(n) novel then show a(n+1) in blue, else a(n) is a repeat, show a(n+1) (countback) in red. I suspect records will all show red.

## Thanks...

@Carl Love Thanks, works fast. How to adapt for graph? Can code be used to check if a(n)+a(n+1)<=n for n up to some given value?

## Thanks...

@Kitonum  Thanks, it worked very well. Can output be adapted to just give the the sequence of primes p (eg using the seq command)?