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

1,2

Links

Table of n, a(n) for n=1..70.

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.

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

Prog

(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

Crossrefs

Cf. A183542, A183543, A183545.

Sequence in context: A050106 A345917 A303739 * A219640 A344406 A184164

Adjacent sequences: A183541 A183542 A183543 * A183545 A183546 A183547

Keyword

nonn

Author

Clark Kimberling, Jan 05 2011

Status

approved