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The successive absolute differences of the "mixed" pairs rebuild the starting sequence (see Comments for the definition of a "mixed pair").
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%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