

A118240


The part of n in base phi left of the decimal using a leastgreedy algorithm representation.


3



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
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OFFSET

0,4


COMMENTS

Uses leastgreedy 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 basephi representation of n in Knott's representation which uses the least number of 0's, the most 1's, and in which the righthand portion (see A362919) is finite.  N. J. A. Sloane, May 27 2023


LINKS



EXAMPLE

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


PROG

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=remlphi; count++; }}


CROSSREFS



KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



