[seqfan] a(n) = n iff a(n) is sum of two consecutive terms of S

Eric Angelini Eric.Angelini at kntv.be
Sun Oct 4 18:46:16 CEST 2009

 Hello SeqFans,
 I was looking for a reordering of the natural numbers obeying to those two conditions:

   a) a maximum possible of a(n)'s are equal to n
   b) a(n)=n iff a(n) is the unique sum of two consecutive terms of S

I have build S(1) and S(2) where roughly 50% of the terms are equal to their rank in S (they are in yellow on attached doc.)



S(1) was build filling the "holes" first (with the smallest available integer)
S(2) was build placing the natural numbers first (in the first available "hole")
If I made no mistake (pencil and paper), S(1) comes lexicographically before S(2)
But there might exist an S(3) with more than 50% of the terms at the right place...

Any idea? Corrections?


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