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A094202
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Integers n whose Zeckendorf representation A014417(n) is palindromic.
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3
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0, 1, 4, 6, 9, 12, 14, 22, 27, 33, 35, 51, 56, 64, 74, 80, 88, 90, 116, 127, 145, 158, 174, 184, 197, 203, 216, 232, 234, 276, 294, 326, 368, 378, 399, 425, 441, 462, 472, 493, 519, 525, 546, 572, 588, 609, 611, 679, 708, 760, 828, 847, 915, 944, 988, 1022, 1064, 1090
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OFFSET
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0,3
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REFERENCES
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C. G. Lekkerkerker, Voorstelling van natuurlijke getallen door een som van getallen van Fibonacci, Simon Stevin vol. 29, 1952, pages 190 - 195
E. Zeckendorf, Representation des nombres naturels par une somme de nombres de Fibonacci ou de nombres de Lucas, Bulletin de la Société Royale des Sciences de Liège vol. 41 (1972) pages 179-182.
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LINKS
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Table of n, a(n) for n=0..57.
Ron Knott Fibonacci Bases.
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EXAMPLE
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Fibonacci base columns are ...,8,5,3,2,1 with column entries 0 or 1 and no two consecutive ones (the Zeckendorf representation) so that each n has a unique representation.
E.g. a(4)=12=8+3+1=10101 base Fib; a(5)=14=13+1=100001 base Fib
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MATHEMATICA
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zeck[n_Integer] := Block[{k = Ceiling[ Log[ GoldenRatio, n*Sqrt[5]]], t = n, fr = {}}, While[k > 1, If[t >= Fibonacci[k], AppendTo[ fr, 1]; t = t - Fibonacci[k], AppendTo[fr, 0]]; k-- ]; FromDigits[fr]]; a = {}; Do[z = zeck[n]; If[ FromDigits[ Reverse[ IntegerDigits[z]]] == z, AppendTo[a, n]], {n, 1123}]; a (from Robert G. Wilson v May 29 2004)
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CROSSREFS
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Cf. A035517.
Gives the positions of zeros in A095734. Subsets: A095730, A048757. A006995 gives the integers whose binary expansion is palindromic.
Sequence in context: A122550 A191407 A076083 * A007074 A054087 A079255
Adjacent sequences: A094199 A094200 A094201 * A094203 A094204 A094205
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KEYWORD
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nonn,base
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AUTHOR
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Ron Knott, May 25 2004
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EXTENSIONS
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More terms from Robert G. Wilson v, May 28 2004
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STATUS
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approved
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