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Search: id:A132673
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| A132673 |
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a(1)=1, a(n)=9*a(n-1) 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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1
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| 1, 9, 8, 7, 6, 5, 4, 3, 2, 18, 17, 16, 15, 14, 13, 12, 11, 10, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 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, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37
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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(n)=maximal positive number <a(n-1) not encountered so far, if existing, else a(n)=9*a(n-1).
Also: a(1)=1, a(n)=a(n-1)-1, if a(n-1)-1>0 and has not been encountered so far, else a(n)=9*a(n-1).
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)=(x(1-2x)/(1-x)+9x^2*f'(x^(17/8))+(17/81)*(f'(x^(1/8))-9x-1)/(1-x) where f(x)=sum{k>=0, x^(9^k)} and f'(z)=derivative of f(x) at x=z.
a(n)=(26*9^(r/2)-10)/8-n if both, r and s are even, else a(n)=(107*9^((s-1)/2)-10)/8-n, where r=ceiling(2*log_9((8n+9)/17)) and s=ceiling(2*log_9(8n+9)/8))-1.
a(n)=(9^floor(1+(k+1)/2)+17*9^floor(k/2)-10)/8-n, where k=r if r is odd, else k=s (with respect to r and s above; formally, k=((r+s)-(r-s)*(-1)^r)/2).
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CROSSREFS
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Cf. For formulas concerning a general parameter p (with respect to the recurrence rule ... a(n)=p*a(n-1) ...) see A132374.
Cf. For p=2 to p=10 see A132666-132674.
Adjacent sequences: A132670 A132671 A132672 this_sequence A132674 A132675 A132676
Sequence in context: A089186 A055120 A090671 this_sequence A107927 A019890 A066666
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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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