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

Author

N. J. A. Sloane, May 27 2023

Keywords

• nonn
• base

Comments

The left portion is given in A118240.

Examples

			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
		

Links

• 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.]

Crossrefs

Cf. A118240, A362920.