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

Neil Sloane njasloane at gmail.com
Wed Jul 31 18:04:51 CEST 2013


These sequences are new to me, and I think they are probably worth adding
to the OEIS.
Could someone please add them, if they aren't already present?
I'm referring to the following:

The gap count between each discrete prime pair is also that discrete prime.
2,3,5,2,7,3,11,13,5,17,19,23,7,29,31,37,41,43,11,47,53,13,59,61,67,71,73,17,79,83,19,89,97,101,103,23,107,109,113,127,131,137,139,29
Dan

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,...

...

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.

Thanks

Neil


On Mon, Jul 29, 2013 at 10:44 AM, DAN_CYN_J <dan_cyn_j at comcast.net> wrote:

>
>
>
> 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
>
> _______________________________________________
>
> Seqfan Mailing list - http://list. seqfan . eu /
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>



-- 
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com



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