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Search: id:A132664
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| A132664 |
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a(1)=1, a(2)=2, a(n)=a(n-1)+n if the minimal natural number not encountered so far is greater than a(n-1), else a(n)=a(n-1)-1. |
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+0
4
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| 1, 2, 5, 4, 3, 9, 8, 7, 6, 16, 15, 14, 13, 12, 11, 10, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48
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OFFSET
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1,2
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COMMENT
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Also: a(1)=1, a(2)=2, a(n)=maximal positive number <a(n-1) not encountered so far, if existing, else a(n)=a(n-1)+n.
Also: a(1)=1, a(2)=2, a(n)=a(n-1)-1, if a(n-1)-1>0 and has not been encountered so far, else a(n)=a(n-1)+n.
A reordering of the natural numbers. The sequence is self-inverse, in that a(a(n))=n.
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FORMULA
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G.f.: g(x)=(L'(x)-x^2-1/(1-x))/(1-x) where L(x)=sum{k>=0, x^(Lucas(k)} and Lucas(k)=A000032(k). L(x) is the g.f. of the Lucas indicator sequence (see A102460) and L'(x)=derivative of L(x).
a(n)=Lucas(Lucas_inverse(n+1)+2)-n-3=A000032(A130241(n+1)+2)-n-3 for n>1.
a(n)=A000032(floor(log_phi(n+3/2)+2)-n-3 for n>1, where phi=(1+sqrt(5))/2 is the golden ratio.
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CROSSREFS
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Cf. A000032, A102460, A130241.
For an analogue concerning Fibonacci numbers see A132665.
See A132666-132674 for sequences with a similar recurrence rule.
Sequence in context: A128173 A060125 A115303 this_sequence A072029 A065652 A083798
Adjacent sequences: A132661 A132662 A132663 this_sequence A132665 A132666 A132667
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KEYWORD
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nonn
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AUTHOR
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Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 15 2007
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