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Search: id:A132665
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| A132665 |
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a(1)=1, a(2)=3, 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, 3, 2, 6, 5, 4, 11, 10, 9, 8, 7, 19, 18, 17, 16, 15, 14, 13, 12, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69
(list; graph; listen)
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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)=3, 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)=3, 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)=(F'(x)-x^2-1/(1-x))/(1-x) where F(x)=sum{k>=0, x^(Fib(k)} and Fib(k)=A000045(k). F(x) is the g.f. of the Fibonacci indicator sequence (see A104162) and F'(x)=derivative of F(x).
a(n)=Fib(Fib_inverse(n+1)+2)-n-3=A000045(A130233(n+1)+2)-n-3.
a(n)=A000032(floor(log_phi(sqrt(5)*(n+1)+1)+2))-n-3, where phi=(1+sqrt(5))/2 is the golden ratio.
a(n)=A000032(floor(log_phi(sqrt(5)*n+2*phi)+2))-n-3.
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CROSSREFS
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Cf. A000045, A104152, A130233.
For an analogue concerning Lucas numbers see A132664.
See A132666-132674 for sequences with a similar recurrence rule.
Sequence in context: A038722 A145522 A131968 this_sequence A132667 A133729 A118833
Adjacent sequences: A132662 A132663 A132664 this_sequence A132666 A132667 A132668
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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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