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.
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
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Mar 10 2011
STATUS
approved