cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

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

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Mar 10 2011

Keywords

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.

Examples

			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..

Crossrefs

A187224, A187470, A187471.

Programs

  • 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 *)

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

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Mar 10 2011

Keywords

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.

Examples

			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..

Crossrefs

A187224, A187469, A187471.

Programs

  • 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 *)
Showing 1-2 of 2 results.

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