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

Hans Havermann gladhobo at teksavvy.com
Mon Jul 29 14:52:06 CEST 2013


Andrew Weimholt:

>> 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,...

http://oeis.org/A026272 (and, adding zeros, http://oeis.org/A193564 ). Not *any* subset surely. Some will run into the issue of having to place a second copy in a position already occupied.


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