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A130245
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Number of Lucas numbers (A000032) <= n.
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10
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0, 1, 2, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Partial sums of the Lucas indicator sequence A102460. For n>=2, we have a(A000032(n))=n+1.
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FORMULA
| a(n)=1+floor(log_phi((n+sqr(n^2+4))/2))=1+floor(arsinh(n/2)/ln(phi)) for n>=2, where phi=(1+sqr(5))/2.
a(n)=A130241(n)+1=A130242(n+1) for n>=2.
G.f.: g(x)=1/(1-x)*sum{k>=0, x^Lucas(k)}.
a(n)=1+floor(log_phi(n+1/2)) for n>=1, where phi is the golden ratio.
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EXAMPLE
| a(9)=5 because there are 5 Lucas numbers <=9 (2,1,3,4 and 7).
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CROSSREFS
| For partial sums see A130246. Other related sequences: A000032, A130241, A130242, A130247, A130249, A130253, A130255, A130259. Indicator sequence A102460. Fibonacci inverse see A130233 - A130240, A104162, A108852.
Sequence in context: A087827 A136528 A130242 * A087793 A030411 A194817
Adjacent sequences: A130242 A130243 A130244 * A130246 A130247 A130248
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KEYWORD
| nonn
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AUTHOR
| Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 19 2007, Jul 02 2007
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