A183542 -id:A183542 - cp's OEIS frontend

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

Clark Kimberling, Jan 05 2011

nonn

Cf. A183542, A183543, A183545.

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

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

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.

A183543 Second of two complementary trees generated by the Wythoff sequences.

Original entry on oeis.org

3, 6, 11, 10, 18, 19, 32, 17, 29, 30, 50, 31, 52, 53, 87, 28, 47, 48, 79, 49, 81, 82, 134, 51, 84, 85, 139, 86, 141, 142, 231, 46, 76, 77, 126, 78, 128, 129, 210, 80, 131, 132, 215, 133, 217, 218, 354, 83, 136, 137, 223, 138, 225, 226, 367, 140, 228, 229, 372, 230, 374, 375, 608

Offset: 1

Clark Kimberling, Jan 05 2011

See A183542.

			First three levels:
...............3
.......6.............11
....10...18.......19....32

Cf. A074049, A183542, A183545.

See the formulas as A074049 and A183545.

A183545 Ordering of the numbers in the tree A183543; complement of A183544.

Original entry on oeis.org

3, 6, 10, 11, 17, 18, 19, 28, 29, 30, 31, 32, 46, 47, 48, 49, 50, 51, 52, 53, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 198, 199, 200

Offset: 1

Clark Kimberling, Jan 05 2011

nonn

Cf. A183542, A183543, A183544.

 nn=200; g=(1+5^(1/2))/2; t={3}; t0=t; While[t=Select[Union[t,-2+Floor[(t+2)g],t+Floor[(t+2)g]], #<=nn&]; t0 !=t, t0=t]; t

The monotonic ordering of the numbers in the set S generated by these rules: 3 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.

cp's OEIS Frontend

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

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A183543 Second of two complementary trees generated by the Wythoff sequences.

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Formula

A183545 Ordering of the numbers in the tree A183543; complement of A183544.

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Author

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Mathematica

Formula