A183544 Ordering of the numbers in the tree A183542; complement of A183545.

1, 2, 4, 5, 7, 8, 9, 12, 13, 14, 15, 16, 20, 21, 22, 23, 24, 25, 26, 27, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103

Offset: 1

Author

Clark Kimberling, Jan 05 2011

Keywords

• nonn

Crossrefs

Cf. A183542, A183543, A183545.

Programs

Mathematica

nn=200; g=(1+5^(1/2))/2; t={1}; t0=t; While[t=Select[Union[t,-2+Floor[(t+2)g], t+Floor[(t+2)g]], #<=nn&]; t0 !=t, t0=t];t

Python

from itertools import islice
def A183544_gen(): # generator of terms
    a, b, i = 1, 1, 0
    while True:
        yield from (j+a for j in range(i,i+a))
        i += a
        a, b = b, a+b
A183544_list = list(islice(A183544_gen(),30)) # Chai Wah Wu, Oct 13 2022

Formula

The monotonic ordering of the numbers in the set S generated by these rules: 1 is in S, and if n is in S, then -2+Floor[(n+2)r] and n+Floor[(n+2)r] are in S, where r=(1+sqrt(5))/2, the golden ratio.