A187470 - OEIS

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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

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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 *)