A173028 Partition of the row numbers of the Wythoff array W: two numbers are in the same row if and only if their rows in W have (essentially) a common divisor greater than 1.

1, 3, 2, 4, 9, 6, 5, 13, 29, 7, 16, 45, 43, 35, 8, 19, 56, 57, 52, 15, 10, 22, 67, 186, 181, 58, 51, 11, 25, 78, 223, 226, 77, 199, 55, 12, 28, 89, 260, 271, 96, 265, 82, 61, 14, 31, 262, 297, 316, 115, 331, 109, 91, 71, 17, 34, 291, 334, 361, 351, 397, 136, 317, 106, 87, 18

Offset

1,2

Comments

(Row 1) = A173027, (Row 2) = A220249. Every positive integer occurs exactly once, so that, as a sequence, this is a permutation of the natural numbers.

Links

Table of n, a(n) for n=1..66.

Formula

Let R(n,k) be the number in row n, column k. After Row 1 (A173027),

inductively, R(n,1) is the least positive integer not in the first n-1

rows, and the rest of row n consists of the numbers of rows X of the

Wythoff array W for X a multiple of a tail of row R(n,1) of W.

Example

First four rows of R:
1...3....4....5.....16....19....22...25...28...
2...9....13...45....56....67....78...89...262..
6...29...43...57....186...223...260..297..334...
7...35...52...181...226...271...316..361..1063...
For example, row 3 begins with 6, which is the least positive
integer not in rows 1 and 2. Row 6 of W is (14,23,37,60,...)
Row 29 of W is (74,120,194,...) = 2*(37,60,97...).
Row 43 of W is (111,180,291,...) = 3*(37,60,97,...).
So row 3 of R begins with (6,29,43...) as there are no other rows
of W numbered <43 which are multiples of row 6 of W.

Crossrefs

Cf. A000045, A035513, A173027, A220249.

Sequence in context: A325909 A270701 A083762 * A360415 A264985 A265355

Adjacent sequences: A173025 A173026 A173027 * A173029 A173030 A173031

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 07 2010

Extensions

Corrections (these have been made): a(31) should read 223 instead of 225, a(63) 317 instead of 314 - K. G. Stier, Dec 21 2012

Status

approved