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

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

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