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A132666
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a(1)=1, a(n)=2*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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19
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1, 2, 4, 3, 6, 5, 10, 9, 8, 7, 14, 13, 12, 11, 22, 21, 20, 19, 18, 17, 16, 15, 30, 29, 28, 27, 26, 25, 24, 23, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Also: a(1)=1, a(n)=maximal positive number <a(n-1) not encountered so far, if existing, else a(n)=2*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)=2*a(n-1).
A reordering of the natural numbers. The sequence is self-inverse in that a(a(n))=n.
Almost certainly a duplicate of A132340. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 12 2008
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers
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FORMULA
| G.f.: g(x)=(x(1-2x)/(1-x)+2x^2*f'(x^3)+3/4*(f'(x)-2x-1))/(1-x) where f(x)=sum{k>=0, x^(2^k)} and f'(z)=derivative of f(x) at x=z.
a(n)=5*2^(r/2)-3-n, if both r and s are even, else a(n)=7*2^((s-1)/2)-3-n, where r=ceiling(2*log_2((n+2)/3)) and s=ceiling(2*log_2((n+2)/2)-1).
a(n)=2^floor(1+(k+1)/2)+3*2^floor(k/2)-3-n, where k=r, if r is even, else k=s (with respect to r and s above; formally, k=((r+s)+(r-s)*(-1)^r)/2).
a(n)=A027383(m)+A027383(m+1)+1-n, where m:=max{ k | A027383(k)<n }.
a(A027383(n)+1)=A027383(n+1).
a(A027383(n))=A027383(n-1)+1 for n>0.
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MATHEMATICA
| max = 72; f[x_] := Sum[x^(2^k), {k, 0, Ceiling[ Log[2, max]]}]; g[x_] = (x (1 - 2x)/(1 - x) + 2x^2*f'[x^3] + 3/4*(f'[x] - 2x - 1))/(1 - x); Drop[ CoefficientList[ Series[ g[x], {x, 0, max}], x], 1] (* From Jean-François Alcover, Dec 01 2011 *)
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PROG
| (Haskell)
import Data.List (delete)
a132666 n = a132666_list !! (n-1)
a132666_list = 1 : f 1 [2..] where
f z xs = y : f y (delete y xs) where
y | head xs > z = 2 * z
| otherwise = z - 1
-- Reinhard Zumkeller, Sep 17 2001
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CROSSREFS
| For formulae concerning a general parameter p (with respect to the recurrence rule ... a(n)=p*a(n-1) ...) see A132374.
For p=3 to p=10 see A132667-132674.
For a similar recurrence rule concerning Fibonacci (A000045) and Lucas numbers (A000032) see A132664 and A132665.
Cf. A027383.
Sequence in context: A091857 A180625 A132340 * A116533 A087559 A193298
Adjacent sequences: A132663 A132664 A132665 * A132667 A132668 A132669
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KEYWORD
| nonn,nice
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AUTHOR
| Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Aug 24 2007, Sep 15 2007
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