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A187471 Array: seven joint rank sequences tending to A184413, by columns.

%I A187471 #9 Dec 04 2016 19:46:24
%S A187471 1,1,1,1,1,1,1,3,3,3,3,3,3,3,6,5,5,5,5,5,5,8,6,6,6,6,6,6,11,8,9,9,9,9,
%T A187471 9,13,9,10,10,10,10,10,15,11,12,11,11,11,11,18,12,14,14,14,14,14,20,
%U A187471 14,16,15,16,16,16,23,16,18,17,17,17,17,25,17,20,19,19,19,19,27,19,21
%N A187471 Array: seven joint rank sequences tending to A184413, by columns.
%C A187471 Precedents are discussed at A187224: adjusted joint rank sequence (AJRS) and the rank transform.
%C A187471 Let W=A001951, so that W(n)=floor[n*sqrt(2)].
%C A187471 Row 1 of A187471 is the AJRS of W and the natural number sequence, A000027.  Row 2 is the AJRS of W and row 1; row 3 is the AJRS of W and row 2; etc.  The limit row (not shown) is the rank transform of W, A184413.
%e A187471 The array consists of seven sequences:
%e A187471 1..3..6..8..11..13..15..18..20..23..25..27..30..32..35..37..
%e A187471 1..3..5..6..8...9...11..12..14..16..17..19..20..22..24..25..
%e A187471 1..3..5..6..9...10..12..14..16..18..20..21..24..25..28..29..
%e A187471 1..3..5..6..9...10..11..14..15..17..19..20..22..24..26..28..
%e A187471 1..3..5..6..9...10..11..14..16..17..19..21..23..24..27..28..
%e A187471 1..3..5..6..9...10..11..14..16..17..19..20..23..24..26..28..
%e A187471 1..3..5..6..9...10..11..14..16..17..19..20..23..24..27..28..
%t A187471 r = 2^(1/2);
%t A187471 seqA = Table[Floor[r*n], {n, 1, 120}];  (* A000201 *)
%t A187471 seqB = Table[n, {n, 1, 120}]jointRank[{seqA_, seqB_}] := {Flatten@Position[#1, {_, 1}],
%t A187471 Flatten@Position[#1, {_, 2}]} & [Sort@Flatten[{{#1, 1} & /@ seqA, {#1, 2} & /@seqB}, 1]]; (#1[[1]] &) /@
%t A187471 FixedPointList[jointRank[{seqA, #1[[1]]}] &, jointRank[{seqA, seqB}], 6];
%t A187471 TableForm[%]
%t A187471 (* by _Peter J. C. Moses_, Mar 10 2011 *)
%Y A187471 Cf. A187224, A187469, A187470.
%K A187471 nonn,tabf
%O A187471 1,8
%A A187471 _Clark Kimberling_, Mar 10 2011