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Search: id:A089961
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| A089961 |
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A sequence having both Fibonacci and Lucas numbers, in n = Lucas and Fibonacci positions. |
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+0
2
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| 3, 4, 7, 3, 11, 3, 3, 18, 3, 5, 5, 3, 29, 3, 4, 9, 3, 8, 4, 3, 47, 3, 4, 6, 3, 14, 3, 3, 13, 3, 6, 4, 3, 76, 3, 3, 4, 7, 3, 9, 3, 3, 23, 3, 5, 5, 3, 21, 3, 3, 10, 3, 7, 4, 3, 123
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n) with n = Fibonacci numbers = corresponding Lucas numbers. a(n) with n = Lucas numbers = corresponding Fibonacci numbers. Examples: a(8) = 18, where 8 = F6 and 18 = L6. a(29) = 13, where 29 = L7 and 13 = F7.
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FORMULA
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1. a(n) = (A0899590(n) - 1). 2. a(n) = floor(1/({n*k}*(1 - {n*k})))- 1; where {x} = fractional part of x; k = phi^(-1).
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EXAMPLE
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1. a(5) = 11 = A089959(5) - 1.
2. a(5) = 11. Take 5*.6180339.. = 3.09169945...= x, then {x} = .090169945...; with k = (3 - sqrt(5))/2 = .6180339...; Floor({n*k}*(1 - {n*k}) = 12. Then subtract 1, getting 11.
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CROSSREFS
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Cf. A089959.
Sequence in context: A130880 A026248 A082089 this_sequence A161775 A109823 A071051
Adjacent sequences: A089958 A089959 A089960 this_sequence A089962 A089963 A089964
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KEYWORD
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nonn,uned
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 20 2003
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