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 A105424 The part of n in base phi left of the decimal point, using a greedy algorithm representation. 10
 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. 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 KEYWORD nonn,base AUTHOR Bryan Jacobs (bryanjj(AT)gmail.com), Apr 08 2005 STATUS approved

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Last modified March 28 03:48 EDT 2023. Contains 361577 sequences. (Running on oeis4.)