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A362919
a(n) is the right portion (reversed) of the base-phi representation of n in Knott's representation which uses the least number of 0's, the most 1's, and in which the right-hand portion is finite.
2
0, 0, 11, 1111, 1111, 1111, 1110, 111101, 111101, 111101, 111111, 111111, 111111, 111110, 111011, 111011, 111011, 111010, 11110101, 11110101, 11110101, 11110111, 11110111, 11110111, 11110110, 11111101, 11111101, 11111101, 11111111, 11111111, 11111111
OFFSET
0,3
COMMENTS
The left portion is given in A118240.
LINKS
Ron Knott, Phigits and the Base Phi representation [Local copy, pdf only]
Jeffrey Shallit, Proving Properties of phi-Representations with the Walnut Theorem-Prover, arXiv:2305.02672 [math.NT], 2023. [Note that this document has been revised multiple times.]
EXAMPLE
The representations of the numbers 0 though 30 are:
0 = 0.0
1 = 1.0
2 = 1.11
3 = 10.1111
4 = 11.1111
5 = 101.1111
6 = 111.0111
7 = 1010.101111
8 = 1011.101111
9 = 1101.101111
10 = 1110.111111
11 = 1111.111111
12 = 10101.111111
13 = 10111.011111
14 = 11010.110111
15 = 11011.110111
16 = 11101.110111
17 = 11111.010111
18 = 101010.10101111
19 = 101011.10101111
20 = 101101.10101111
21 = 101110.11101111
22 = 101111.11101111
23 = 110101.11101111
24 = 110111.01101111
25 = 111010.10111111
26 = 111011.10111111
27 = 111101.10111111
28 = 111110.11111111
29 = 111111.11111111
30 = 1010101.11111111
CROSSREFS
Sequence in context: A127851 A135656 A130602 * A289372 A289101 A289401
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, May 27 2023
STATUS
approved