[seqfan] Re: A prime sequence that contains each sequential prime twice.

DAN_CYN_J dan_cyn_j at comcast.net
Mon Jul 29 16:44:30 CEST 2013




Andrew, 

  

Thanks for your input. 

  

I did do the 3 bagger with the natural numbers but it had restrictions and appears to 

work ------- 

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,---oo? 
The restriction being, if any smaller integer landed on the same 

location then the larger integer would have (1) more added to its 

gap. Neither smaller nor larger integer can ever have more then one 

addition to it's gap. 

So a possibility of a failure. 

  

Thanks, 

  

Dan 



From: "Andrew Weimholt " < andrew . weimholt @ gmail .com> 
To: "Sequence Fanatics Discussion list" < seqfan @list. seqfan . eu > 
Sent: Monday, July 29, 2013 7:22:36 AM 
Subject: [ seqfan ] Re: A prime sequence that contains each sequential prime        twice. 

On Sun, Jul 28, 2013 at 12:16 PM, DAN_ CYN _J < dan _ cyn _j at comcast.net> wrote: 
> 
> The gap count between each discrete prime pair is also that discrete 
prime. 
> 
>2,3,5,2,7,3,11,13,5,17,19,23,7,29,31,37... 
> 

There's nothing really special about this sequence. 
Any subset of the natural numbers can be used to create a sequence where 
a) every term appears twice 
b) the first appearance of each term occurs in their natural order 
c) the number of terms between like terms is the value of that term. 
 i.e. a(n+1+a(n))=a(n) 

Here's an example with the natural numbers... 
1,2,1,3,2,4,5,3,6,7,4,... 

And here's an example with the squares... 
1,4,1,9,16,25,4,... 

Again, nothing special. 
I don't think this type of sequence is worth including in the OEIS . 

Andrew 

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