OFFSET
0,3
LINKS
T. D. Noe, Table of n, a(n) for n = 0..1000
F. Michel Dekking, How to add two natural numbers in base phi, arXiv:2002.01665 [math.NT], 5 Feb 2020.
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
2 = 10.01 in base phi, so left of the decimal point is 10.
The first few numbers written in base phi:
0 = 0.
1 = 1.
2 = 10.01
3 = 100.01
4 = 101.01
5 = 1000.1001
6 = 1010.0001
7 = 10000.0001
8 = 10001.0001
9 = 10010.0101
10 = 10100.0101
11 = 10101.0101
12 = 100000.101001
13 = 100010.001001
14 = 100100.001001
15 = 100101.001001
16 = 101000.100001
17 = 101010.000001
18 = 1000000.000001
19 = 1000001.000001
20 = 1000010.010001
21 = 1000100.010001
22 = 1000101.010001
23 = 1001000.100101
24 = 1001010.000101
...
MATHEMATICA
nn = 1000; len = 2*Ceiling[Log[GoldenRatio, nn]]; Table[d = RealDigits[n, GoldenRatio, len]; FromDigits[Take[d[[1]], d[[2]]]], {n, 0, nn}] (* T. D. Noe, May 20 2011 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Bryan Jacobs (bryanjj(AT)gmail.com), Apr 08 2005
EXTENSIONS
Definition clarified by N. J. A. Sloane, May 27 2023
STATUS
approved