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.

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

Table of n, a(n) for n=0..30.

Ron Knott, Phigits and the Base Phi representation.

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

Cf. A118240, A362920.

Sequence in context: A127851 A135656 A130602 * A289372 A289101 A289401

Adjacent sequences: A362916 A362917 A362918 * A362920 A362921 A362922

Keyword

nonn,base

Author

N. J. A. Sloane, May 27 2023

Status

approved