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A050140
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a(n) = 2*floor(n*phi)-n, where phi = (1+sqrt(5))/2.
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7
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1, 4, 5, 8, 11, 12, 15, 16, 19, 22, 23, 26, 29, 30, 33, 34, 37, 40, 41, 44, 45, 48, 51, 52, 55, 58, 59, 62, 63, 66, 69, 70, 73, 76, 77, 80, 81, 84, 87, 88, 91, 92, 95, 98, 99, 102, 105, 106, 109, 110, 113, 116, 117, 120, 121, 124, 127, 128, 131, 134, 135, 138, 139
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OFFSET
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1,2
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COMMENTS
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Old name was a(n) = last number in repeating block in continued fraction for n*phi.
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REFERENCES
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Alfred Brousseau, Fibonacci and Related Number Theoretic Tables, The Fibonacci Association, 1972, 101-103.
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LINKS
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FORMULA
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a(n) = -n + 2*floor(n*phi) = A283233(n)-n.
a(n) = floor(n*phi) + floor(n*sigma) where phi = (sqrt(5)+1)/2 and sigma = (sqrt(5)-1)/2.
a(n) = last number in repeating block in continued fraction for n*phi.
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MATHEMATICA
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Table[-n+2Floor[n*GoldenRatio], {n, 1, 100}]
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PROG
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(PARI) for(n=1, 50, print1(-n + 2*floor(n*(1+sqrt(5))/2), ", ")) \\ G. C. Greubel, Oct 15 2017
(Magma) [-n + 2*Floor(n*(1+Sqrt(5))/2): n in [1..50]]; // G. C. Greubel, Oct 15 2017
(Python)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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