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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 18 03:09 EST 2021. Contains 340249 sequences. (Running on oeis4.)