A187470 Array: five joint rank sequences tending to A187413, by columns.

1, 1, 1, 1, 1, 4, 3, 3, 3, 3, 6, 4, 5, 5, 5, 9, 6, 7, 7, 7, 12, 8, 9, 9, 9, 14, 9, 11, 10, 10, 17, 11, 13, 12, 13, 19, 12, 15, 14, 14, 22, 14, 17, 16, 16, 25, 16, 19, 18, 18, 27, 17, 21, 19, 20, 30, 19, 23, 21, 22, 33, 21, 25, 23, 24, 35, 22, 27, 25, 26, 38, 24, 29, 27, 28, 40, 25, 31, 28, 29

Offset

1,6

Comments

Precedents are discussed at A187224: adjusted joint rank sequence (AJRS) and the rank transform.

Row 1 (A003622, odds) is the AJRS of the lower Wythoff sequence (A000201) and the natural number sequence, A000027. Row 2 (A000201) is the AJRS of A000201 and row 1; row 3 (A005408) is the AJRS of A000201 and row 2; etc. The limit row (not shown) is the rank transform of A000201, which is A187413. The array shows the first five AJRSs and indicates fairly rapid convergence.

Links

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

Example

The array consists of five sequences:
1..4..6..9..12..14..17..19..22..25..27..30..33..35..38..40..
1..3..4..6..8...9...11..12..14..16..17..19..21..22..24..25..
1..3..5..7..9...11..13..15..17..19..21..23..25..27..29..31..
1..3..5..7..9...10..12..14..16..18..19..21..23..25..27..28..
1..3..5..7..9...10..13..14..16..18..20..22..24..26..28,,29..

Mathematica

r = (1 + 5^(1/2))/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}], 4];
TableForm[%]
(* by Peter J. C. Moses, Mar 10 2011 *)

Crossrefs

A187224, A187469, A187471.

Sequence in context: A031353 A356764 A085415 * A374419 A059124 A320604

Adjacent sequences: A187467 A187468 A187469 * A187471 A187472 A187473

Keyword

nonn,tabf

Author

Clark Kimberling, Mar 10 2011

Status

approved