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Search: id:A050140
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| A050140 |
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a(n) = last digit in repeating block in continued fraction for n*tau. |
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+0
3
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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
(list; graph; listen)
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OFFSET
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1,2
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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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FORMULA
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a(n)=floor(n*tau)+floor(n*sigma) where tau=(sqrt(5)+1)/2 and sigma=(sqrt(5)-1)/2.
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EXAMPLE
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a(6) = 12 because 6*tau = 9 + 1/(1 + 1/(2 + 1/(2 + 1/(2 + 1/(1 + 1/(12 + 1/(1 + 1/(2 + 1/(2 + 1/(2 + 1/(1 + 1/(12 + 1/(1 + 1/(2 + 1/(2 + 1/(2 + 1/(1 + 1/(12 + 1/(1 + ...))))))))))))))))))).
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CROSSREFS
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Cf. A000201, A005206, A050141, A005614, A001350.
Sequence in context: A116050 A056721 A057479 this_sequence A047376 A117573 A144062
Adjacent sequences: A050137 A050138 A050139 this_sequence A050141 A050142 A050143
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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)
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EXTENSIONS
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Formula and more terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 23 2001
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