[seqfan] Absolute diff and sums not to be shared

[Eric Angelini]

Hello SeqFans,
We want S to be a permutation of the integers >0;
We want S to be the lexicographically first seq of its kind (see below);
If we take two adjacent integers of S, say p & q, we want that:
-> no other pair of adjacent integers in S shares the abs. diff. |p-q|
-> no other pair of adjacent integers in S shares the sum (p+q)
-> no |p-q|=(p'+q') with p'and q' being two other adjacent integers in S.

So S is extended with the smallest integer n such that neither |(n-1)-n|
nor [(n-1)+n] has occurred before as a sum or as a diff. of two adjacent
integers in S.

  Sum  3  6  12 11 13  28  27 32  29 22
S(n)= 1  2  4  8  3  10  18  9  23  6  16 ...
  Dif  1  2  4  5  7   8   9  14  17 10

Hope this is not old hat,
Best,
É.