login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A118240 The part of n in base phi left of the decimal using a least-greedy 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
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
LINKS
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
6 = 111.01101010... in base phi using the least-greedy 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=rem-lphi; count++; }}
CROSSREFS
Sequence in context: A368804 A037090 A171676 * A157845 A230297 A086084
KEYWORD
nonn,base
AUTHOR
Graeme McRae, Apr 17 2006
EXTENSIONS
a(1) corrected by N. J. A. Sloane, May 27 2023
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 24 15:37 EDT 2024. Contains 371960 sequences. (Running on oeis4.)