%I #30 Aug 31 2016 15:19:43
%S 1,2,3,5,7,9,4,6,8,10,12,14,11,13,17,19,23,18,15,16,20,21,22,24,25,26,
%T 27,28,30,32,33,34,35,36,29,31,37,41,43,47,38,39,40,42,44,45,46,48,49,
%U 50,51,52,54,55,56,57,53,59,61,67,71,65,58,60,62,63,64,66,68,69,70,72,74,75,76,77,78,80,81,73,79,83,89,97,87,82,84,85,86,88,90,91,92
%N The successive absolute differences of the "mixed" pairs rebuild the starting sequence (see Comments for the definition of a "mixed pair").
%C A "mixed pair" happens when a(n) and a(n+1) share exactly one prime.
%C The sequence starts with a(1) = 1 and is always extended with the
%C smallest integer not yet used that doesn't lead to a contradiction.
%C The sequence is a permutation of the natural numbers.
%H Jean-Marc Falcoz, <a href="/A276227/b276227.txt">Table of n, a(n) for n = 1..4002</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e The "mixed pairs" are between parentheses:
%e (1,2),3,5,(7,9),4,6,8,10,12,(14,11),13,17,19,(23,18),15,16,20,21,22,24,25,26,27,28,30,32,33,34,35,(36,29),...
%e Listing the absolute differences of those parentheses gives: (1),(2),(3),(5),(7),... which is indeed the starting sequence.
%K nonn,base
%O 1,2
%A _Eric Angelini_ and _Jean-Marc Falcoz_, Aug 29 2016