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Search: id:A134859
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| 1, 6, 9, 14, 19, 22, 27, 30, 35, 40, 43, 48, 53, 56, 61, 64, 69, 74, 77, 82, 85, 90, 95, 98, 103, 108, 111, 116, 119, 124, 129, 132, 137, 142, 145, 150, 153, 158, 163, 166, 171, 174, 179, 184, 187, 192, 197, 200, 205, 208, 213, 218, 221, 226, 229, 234, 239, 242
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OFFSET
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1,2
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COMMENT
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The lower and upper Wythoff sequences, A and B, satisfy the complementary equations AAA=AB-2 and AAA=A+B-2.
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REFERENCES
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C. Kimberling, Complementary equations and Wythoff sequences, preprint, 2007.
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FORMULA
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a(n)=A(A(A(n))), n>=1, with A=A000201, the lower Wythoff sequence.
a(n)=2*floor(n*Phi^2)+n-2 where Phi=(1+sqrt(5))/2 - Benoit Cloitre (benoit7848c@orange.fr), Apr 12 2008, R. J. Mathar, Oct 16 2009
a(n) = A095098(n-1), n>1. R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 16 2009
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EXAMPLE
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Starting with A=(1,3,4,6,8,9,11,12,14,16,17,19,...), we have A(2)=3, so A(A(2))=4, so A(A(A(2)))=6.
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CROSSREFS
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Cf. A000201, A001950, A003622, A003623, A035336, A101864, A134860, A035337, A134861, A134862, A134863, A035338, A134864, A035513.
Sequence in context: A133796 A129413 A095098 this_sequence A154778 A106350 A020717
Adjacent sequences: A134856 A134857 A134858 this_sequence A134860 A134861 A134862
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Nov 14 2007
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EXTENSIONS
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Corrected formula, removed associated incorrect PARI program - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 16 2009
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