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A187470
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Array: five joint rank sequences tending to A187413, by columns.
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2
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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
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OFFSET
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1,6
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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..
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MATHEMATICA
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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[%]
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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