

A141106


Lower Odd Swappage of Upper Wythoff Sequence.


4



1, 5, 7, 9, 13, 15, 17, 19, 23, 25, 27, 31, 33, 35, 39, 41, 43, 47, 49, 51, 53, 57, 59, 61, 65, 67, 69, 73, 75, 77, 81, 83, 85, 89, 91, 93, 95, 99, 101, 103, 107, 109, 111, 115, 117, 119, 123, 125, 127, 129, 133, 135, 137, 141, 143, 145, 149, 151, 153, 157, 159, 161, 163
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OFFSET

1,2


COMMENTS

1. lim (1/n)*A141106(n) = 1 + tau
2. Let S(n)=(1/2)*(1+A141106(n)). Is the complement of S equal to A035487?


LINKS

Table of n, a(n) for n=1..63.


FORMULA

Let a = (1,3,4,6,8,9,11,12,...) = A000201 = lower Wythoff sequence; let b = (2,5,7,10,13,15,18,...) = A001950 = upper Wythoff sequence. For each even b(n), let a(m) be the least number in a such that after swapping b(n) and a(m), the resulting new a and b are both increasing. A141106 is the sequence obtained by thus swapping all evens out of A001950.


EXAMPLE

Start with
a = (1,3,4,6,8,9,11,12,...) and b = (2,5,7,10,13,15,18,...).
After 1st swap,
a = (2,3,4,6,8,9,11,12,...) and b = (1,5,7,10,13,15,18,...).
After 2nd swap,
a = (2,3,4,5,6,9,11,12,...) and b = (1,5,7,9,13,15,18,...).


CROSSREFS

Cf. A000201, A001950, A141104, A141105, A141107, A004976.
Sequence in context: A200268 A251627 A128161 * A047478 A048974 A089193
Adjacent sequences: A141103 A141104 A141105 * A141107 A141108 A141109


KEYWORD

nonn


AUTHOR

Clark Kimberling, Jun 02 2008


STATUS

approved



