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A132666 a(1)=1, a(n) = 2*a(n-1) if the minimal positive integer not yet in the sequence is greater than a(n-1), else a(n) = a(n-1)-1.

%I A132666 #25 Aug 09 2017 23:07:39
%S A132666 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,
%T A132666 26,25,24,23,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,62,61,60,
%U A132666 59,58,57,56,55,54,53,52,51,50,49,48,47,94,93,92,91,90,89,88,87,86,85
%N A132666 a(1)=1, a(n) = 2*a(n-1) if the minimal positive integer not yet in the sequence is greater than a(n-1), else a(n) = a(n-1)-1.
%C A132666 Also: a(1)=1, a(n) = maximal positive number < a(n-1) not yet in the sequence, if it exists, else a(n) = 2*a(n-1).
%C A132666 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).
%C A132666 A reordering of the natural numbers. The sequence is self-inverse in that a(a(n)) = n.
%C A132666 Almost certainly a duplicate of A132340. - _R. J. Mathar_, Jun 12 2008
%H A132666 Reinhard Zumkeller, <a href="/A132666/b132666.txt">Table of n, a(n) for n = 1..10000</a>
%H A132666 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A132666 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.
%F A132666 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).
%F A132666 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).
%F A132666 a(n) = A027383(m) + A027383(m+1) + 1 - n, where m:=max{ k | A027383(k) < n }.
%F A132666 a(A027383(n) + 1) = A027383(n+1).
%F A132666 a(A027383(n)) = A027383(n-1) + 1 for n > 0.
%t A132666 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] (* _Jean-François Alcover_, Dec 01 2011 *)
%o A132666 (Haskell)
%o A132666 import Data.List (delete)
%o A132666 a132666 n = a132666_list !! (n-1)
%o A132666 a132666_list = 1 : f 1 [2..] where
%o A132666    f z xs  = y : f y (delete y xs) where
%o A132666      y | head xs > z = 2 * z
%o A132666        | otherwise   = z - 1
%o A132666 -- _Reinhard Zumkeller_, Sep 17 2001
%Y A132666 For formulas concerning a general parameter p (with respect to the recurrence rule ... a(n)=p*a(n-1) ...) see A132674.
%Y A132666 For p=3 to p=10 see A132667 through A132674.
%Y A132666 For a similar recurrence rule concerning Fibonacci (A000045) and Lucas numbers (A000032) see A132664 and A132665.
%Y A132666 Cf. A027383.
%K A132666 nonn,nice
%O A132666 1,2
%A A132666 _Hieronymus Fischer_, Aug 24 2007, Sep 15 2007