cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Views

Author

Clark Kimberling, Jan 05 2011

Keywords

Crossrefs

Cf. A183542, A183543, A183544.

Programs

  • Mathematica
     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

Formula

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.

A183542 First of two complementary trees generated by the Wythoff sequences.

Original entry on oeis.org

1, 2, 5, 4, 8, 9, 16, 7, 13, 14, 24, 15, 26, 27, 45, 12, 21, 22, 37, 23, 39, 40, 66, 25, 42, 43, 71, 44, 73, 74, 121, 20, 34, 55, 58, 36, 60, 61, 100, 38, 63, 64, 105, 65, 107, 108, 176, 41, 68, 69, 113, 70, 115, 116, 189, 72, 118, 119, 194, 120, 196, 197, 320
Offset: 1

Views

Author

Clark Kimberling, Jan 05 2011

Keywords

Comments

Begin with the main tree A074049 generated by the Wythoff sequences:
...................1
...................2
...........3.................5
.......4.......7........8........13
.....6..10...11..18....12..20...21..34
Every n >2 is in the subtree from 3 or the subtree from 5. Therefore, on subtracting 2 from all entries in those subtrees, we obtain complementary trees: A183342 and A183543.

Examples

			First three levels:
...................1
.............2............3
..........4.....8......9.....16

Crossrefs

Cf. A074049, A183543, A183544,
A183079 (definition of tree generated by a sequence).

Formula

See the formulas at A074049 and A183544.

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

Original entry on oeis.org

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

Views

Author

Clark Kimberling, Jan 05 2011

Keywords

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.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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