

A187471


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


3



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, 9, 13, 9, 10, 10, 10, 10, 10, 15, 11, 12, 11, 11, 11, 11, 18, 12, 14, 14, 14, 14, 14, 20, 14, 16, 15, 16, 16, 16, 23, 16, 18, 17, 17, 17, 17, 25, 17, 20, 19, 19, 19, 19, 27, 19, 21
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OFFSET

1,8


COMMENTS

Precedents are discussed at A187224: adjusted joint rank sequence (AJRS) and the rank transform.
Let W=A001951, so that W(n)=floor[n*sqrt(2)].
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.


LINKS

Table of n, a(n) for n=1..80.


EXAMPLE

The array consists of seven sequences:
1..3..6..8..11..13..15..18..20..23..25..27..30..32..35..37..
1..3..5..6..8...9...11..12..14..16..17..19..20..22..24..25..
1..3..5..6..9...10..12..14..16..18..20..21..24..25..28..29..
1..3..5..6..9...10..11..14..15..17..19..20..22..24..26..28..
1..3..5..6..9...10..11..14..16..17..19..21..23..24..27..28..
1..3..5..6..9...10..11..14..16..17..19..20..23..24..26..28..
1..3..5..6..9...10..11..14..16..17..19..20..23..24..27..28..


MATHEMATICA

r = 2^(1/2);
seqA = Table[Floor[r*n], {n, 1, 120}]; (* A000201 *)
seqB = Table[n, {n, 1, 120}]jointRank[{seqA_, seqB_}] := {Flatten@Position[#1, {_, 1}],
Flatten@Position[#1, {_, 2}]} & [Sort@Flatten[{{#1, 1} & /@ seqA, {#1, 2} & /@seqB}, 1]]; (#1[[1]] &) /@
FixedPointList[jointRank[{seqA, #1[[1]]}] &, jointRank[{seqA, seqB}], 6];
TableForm[%]
(* by Peter J. C. Moses, Mar 10 2011 *)


CROSSREFS

Cf. A187224, A187469, A187470.
Sequence in context: A259581 A105592 A210745 * A083565 A237117 A247970
Adjacent sequences: A187468 A187469 A187470 * A187472 A187473 A187474


KEYWORD

nonn,tabf


AUTHOR

Clark Kimberling, Mar 10 2011


STATUS

approved



