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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row 1: A000027 (natural numbers)

Row 2: A000201 (lower Wythoff sequence)

limit-row: 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: A263916 A115131 A210258 * A211782 A211701 A183110

Adjacent sequences:  A181105 A181106 A181107 * A181109 A181110 A181111

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Oct 03 2010

STATUS

approved

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Last modified April 29 22:12 EDT 2017. Contains 285615 sequences.