A181108 Array whose rows result from iterating an algorithm that carries the natural numbers to the lower Wythoff sequence.
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
Offset: 1
Examples
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
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).
Comments