A187469 Array: five joint rank sequences tending to lower Wythoff sequence A000201, by columns.

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

Offset

1,6

Comments

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

Row 1 (A005498, odds) is the AJRS of the natural number sequence N=A000027 with itself. Row 2 is the AJRS of N and row 1; row 3 is the AJRS of N and row 2; etc. The limit row is the rank transform of N, the lower Wythoff sequence, A000201. 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..3..5..7..9..11..13..15..17..19..21..23..25..27..29..31..
1..3..4..6..7..9...10..12..13..15..16..18..19..21..22..24..
1..3..4..6..8..9...11..13..14..16..18..19..21..23..24..26..
1..3..4..5..8..9...11..12..14..16..17..19..20..22..24..25..
1..3..4..6..8..9...11..12..14..16..17..19..21..22..24..25..

Mathematica

seqA = Table[n, {n, 1, 120}];
seqB = seqA;
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, A187470, A187471.

Sequence in context: A147752 A236682 A114227 * A112593 A213809 A204854

Adjacent sequences: A187466 A187467 A187468 * A187470 A187471 A187472

Keyword

nonn,tabf

Author

Clark Kimberling, Mar 10 2011

Status

approved