%I #13 Jun 10 2016 00:20:59
%S 1,3,2,5,9,4,13,19,6,25,32,7,39,47,8,55,65,10,75,86,11,97,109,12,121,
%T 135,14,149,164,15
%N Let S be the sequence and let D denote the sequence obtained by moving every third term three steps to the left. The D is the sequence of absolute values of the first differences of S.
%C We also require that S be a permutation of the natural numbers and the lexicographically earliest sequence with the stated propoerty.
%H Eric Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/Hilbert3n.htm">Hilbert Hotel and 3k rooms</a>
%H E. Angelini, <a href="/A173701/a173701.pdf">Hilbert Hotel and 3k rooms</a> [Cached copy, with permission]
%e Here is S:
%e S = ...1,3,2,5,9,4,13,19,6,25,32,7,39,47,8,55,65,10,75,86,11,97,109,12,121
%e The terms 2,4,6,7, ... move 3 places left.
%e After the moves we have:
%e D = .2,1,3,4,5,9,6,13,19,7,25,32,8,39,47,10,55,65,11,75,86,12,97,109,14,121
%e and D indeed gives the absolute values of the first differences of S.
%K nonn,more
%O 1,2
%A _Eric Angelini_, Nov 25 2010