login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A105424 The part of n in base phi left of the decimal point, using a greedy algorithm representation. 9
0, 1, 10, 100, 101, 1000, 1010, 10000, 10001, 10010, 10100, 10101, 100000, 100010, 100100, 100101, 101000, 101010, 1000000, 1000001, 1000010, 1000100, 1000101, 1001000, 1001010, 1010000, 1010001, 1010010, 1010100, 1010101, 10000000 (list; graph; refs; listen; history; text; internal format)
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]

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

Cf. A055778, A105425, A104605.

See A341722 for the part to the right of the decimal point.

Sequence in context: A185101 A007924 A115794 * A115832 A336611 A342215

Adjacent sequences:  A105421 A105422 A105423 * A105425 A105426 A105427

KEYWORD

nonn,base

AUTHOR

Bryan Jacobs (bryanjj(AT)gmail.com), Apr 08 2005

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 31 16:38 EDT 2021. Contains 346376 sequences. (Running on oeis4.)