

A181108


Array whose rows result from iterating an algorithm that carries the natural numbers to the lower Wythoff sequence.


2



1, 2, 1, 3, 3, 1, 4, 4, 3, 1, 5, 6, 4, 3, 1, 6, 8, 5, 4, 3, 1, 7, 9, 7, 5, 4, 3, 1, 8, 11, 9, 7, 5, 4, 3, 1, 9, 12, 10, 9, 7, 5, 4, 3, 1, 10, 14, 12, 11, 9, 7, 5, 4, 3, 1, 11, 16, 14, 12, 11, 9, 7, 5, 4, 3, 1, 12, 17, 16, 13, 12, 11, 9, 7, 5, 4, 3, 1, 13, 19, 17, 15, 13, 12, 11, 9, 7, 5, 4, 3, 1, 14, 21
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OFFSET

1,2


COMMENTS

Row 1: A000027 (natural numbers)
Row 2: A000201 (lower Wythoff sequence)
limitrow: A003159


LINKS

Table of n, a(n) for n=1..93.


FORMULA

To generate row n+1 from row n, let
(row n) = (s(1), s(2), s(3), ...)
(row n+1) = (t(1), t(2), t(3), ...)
Then for k=1,2,3,..., let
t(k) = least positive integer not yet in sequences t or u
u(k) = t(k) + s(k).


EXAMPLE

Northwest corner:
1...2...3...4...5...6...7....8....9...
1...3...4...6...8...9...11...12...14...
1...3...4...5...7...9...10...12...14...
1...3...4...5...7...9...11...12...13...
To get row 2 from row 1:
s: 1...2...3...4...5....6....7...
t: 1...3...4...6...8....9....11...
u: 2...5...7...10..13...15...18...
To get row 3 from row 2:
s: 1...3...4...6....8....9....11
t: 1...3...4...5....7....9....10
u: 2...6...8...11...15...18...21


CROSSREFS

Cf. A000201, A181108.
Sequence in context: A115131 A263916 A210258 * A211782 A211701 A183110
Adjacent sequences: A181105 A181106 A181107 * A181109 A181110 A181111


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Oct 03 2010


STATUS

approved



