A118241 -id:A118241 - cp's OEIS frontend

A118240 The part of n in base phi left of the decimal using a least-greedy algorithm representation.

0, 1, 1, 10, 11, 101, 111, 1010, 1011, 1101, 1110, 1111, 10101, 10111, 11010, 11011, 11101, 11111, 101010, 101011, 101101, 101110, 101111, 110101, 110111, 111010, 111011, 111101, 111110, 111111, 1010101, 1010111, 1011010, 1011011, 1011101

Offset: 0

Graeme McRae, Apr 17 2006

Uses least-greedy algorithm (start with largest possible power of phi, writing a 1 only when required, then work downward).

a(n) is also the left portion 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 (see A362919) is finite. - N. J. A. Sloane, May 27 2023

			6 = 111.01101010... in base phi using the least-greedy algorithm. The part to the left of the decimal is a(6) = 111.

Ron Knott, Phigits and the Base Phi representation.
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.]

Cf. A055778, A104605, A118241, A105424, A362919, A362920.

constant (float): phi=(sqrt(5)+1)/2;
variable (float): lphi=phi^floor[log(n)/log(phi)];
variable (float): rem=n;
variable (integer): count=0;
loop: while lphi>1 {count=count*10; lphi=lphi/phi; if(rem > lphi*phi) { rem=rem-lphi; count++;}}

a(1) corrected by N. J. A. Sloane, May 27 2023

cp's OEIS Frontend

A118240 The part of n in base phi left of the decimal using a least-greedy algorithm representation.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Pseudocode

Extensions