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Search: id:A132671
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| A132671 |
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a(1)=1, a(n)=7*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, 7, 6, 5, 4, 3, 2, 14, 13, 12, 11, 10, 9, 8, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 105, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92
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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)=7*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)=7*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)+7x^2*f'(x^(13/6))+(13/49)*(f'(x^(1/6))-7x-1)/(1-x) where f(x)=sum{k>=0, x^(7^k)} and f'(z)=derivative of f(x) at x=z.
a(n)=(20*7^(r/2)-8)/6-n if both, r and s are even, else a(n)=(62*7^((s-1)/2)-8)/6-n, where r=ceiling(2*log_7((6n+7)/13)) and s=ceiling(2*log_7(6n+7)/6))-1.
a(n)=(7^floor(1+(k+1)/2)+13*7^floor(k/2)-8)/6-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.
Sequence in context: A004448 A031099 A055118 this_sequence A074921 A120634 A104178
Adjacent sequences: A132668 A132669 A132670 this_sequence A132672 A132673 A132674
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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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