

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.


2



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
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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 n1
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: A099257 A270701 A083762 * A264985 A265355 A265354
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



