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Rank transform of the sequence ceiling(n/3); complement of A187571.
3

%I #14 Feb 12 2014 18:11:47

%S 1,2,3,5,6,7,9,10,11,13,14,15,16,17,18,20,21,22,24,25,26,28,29,30,31,

%T 32,33,35,36,37,39,40,41,43,44,45,46,47,48,50,51,52,54,55,56,58,59,60,

%U 62,63,64,66,67,68,70,71,72,73,74,75,77,78,79,81,82,83,85,86,87,88,89,90,92,93,94,96,97,98,100,101,102,103,104,105,107,108,109,111,112,113,115,116

%N Rank transform of the sequence ceiling(n/3); complement of A187571.

%C Appears to be a duplicate of A045749. - _R. J. Mathar_, Mar 15 2011

%C The Mathematica programs shown at A187570 and A045749 confirm equality of the first 500 terms. - _Clark Kimberling_, Apr 02 2011

%C The sequence of which A187570 is the rank transform is (1,1,1,2,2,2,3,3,3,4,4,4,...), which is (A002264 without the initial three zeros). For a discussion on rank transforms, see A187224.

%t seqA = Table[Ceiling[n/3], {n, 1, 220}] (*A002264*)

%t seqB = Table[n, {n, 1, 220}]; (*A000027*)

%t jointRank[{seqA_, seqB_}] := {Flatten@Position[#1, {_, 1}], Flatten@Position[#1, {_, 2}]} &[Sort@Flatten[{{#1, 1} & /@ seqA, {#1, 2} & /@ seqB}, 1]];

%t limseqU=FixedPoint[jointRank[{seqA, #1[[1]]}] &,

%t jointRank[{seqA, seqB}]][[1]] (*A187570*)

%t Complement[Range[Length[seqA]], limseqU] (*A187571*)

%t (*by _Peter J. C. Moses_, Mar 11 2011*)

%Y Cf. A187224, A187571, A045749, A045750.

%K nonn

%O 1,2

%A _Clark Kimberling_, Mar 11 2011