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A105424
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The part of n in base phi left of the decimal point, using a greedy algorithm representation.
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10
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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
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listen;
history;
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internal format)
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OFFSET
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0,3
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LINKS
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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]
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EXAMPLE
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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
...
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A001622, 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
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KEYWORD
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nonn,base
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AUTHOR
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Bryan Jacobs (bryanjj(AT)gmail.com), Apr 08 2005
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STATUS
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approved
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