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A130600
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Integers written in base phi, with the "decimal point" omitted.
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5
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1, 1001, 10001, 10101, 10001001, 10100001, 100000001, 100010001, 100100101, 101000101, 101010101, 100000101001, 100010001001, 100100001001, 100101001001, 101000100001, 101010000001, 1000000000001, 1000001000001
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This is the "greedy" or "minimal" representation (see also A130601).
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LINKS
| Casey Mongoven and T. D. Noe, Table of n, a(n) for n = 1..1000
Casey Mongoven, Music based on this sequence
Ron Knott, Integers written in base phi
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EXAMPLE
| If the decimal point were included, the sequence would read 1., 10.01, 100.01, 101.01, 1000.1001, 1010.0001, 10000.0001, 10001.0001, 10010.0101, 10100.0101, 10101.0101, ... Unfortunately these are not integers.
Examples: a(2)=1001 because phi^1+phi^-2 = 2, a(3) = 10001 because phi^2+phi^-2 = 3, a(4) = 10101 because phi^2+phi^0+phi^-2 = 4.
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MATHEMATICA
| nn = 100; len = 2*Ceiling[Log[GoldenRatio, nn]]; Table[d = RealDigits[n, GoldenRatio, len]; last1 = Position[d[[1]], 1][[-1, 1]]; FromDigits[Take[d[[1]], last1]], {n, nn}] (* T. D. Noe, May 20 2011 *)
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CROSSREFS
| Cf. A055778, A105424, A130601.
Sequence in context: A044881 A153814 A100709 * A114387 A204965 A192776
Adjacent sequences: A130597 A130598 A130599 * A130601 A130602 A130603
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KEYWORD
| nonn
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AUTHOR
| Casey Mongoven (cm(AT)caseymongoven.com), Aug 06 2007
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