A173701 - OEIS

%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