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A132668 a(1)=1, a(n) = 4*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 A132668 #7 Aug 09 2017 23:07:39
%S A132668 1,4,3,2,8,7,6,5,20,19,18,17,16,15,14,13,12,11,10,9,36,35,34,33,32,31,
%T A132668 30,29,28,27,26,25,24,23,22,21,84,83,82,81,80,79,78,77,76,75,74,73,72,
%U A132668 71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49
%N A132668 a(1)=1, a(n) = 4*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 A132668 Also: a(1)=1, a(n) = maximal positive integer < a(n-1) not yet in the sequence, if it exists, else a(n) = 4*a(n-1).
%C A132668 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) = 4*a(n-1).
%C A132668 A permutation of the positive integers. The sequence is self-inverse, in that a(a(n)) = n.
%F A132668 a(n) = (11*4^(r/2) - 5)/3 - n, if both r and s are even, else a(n) = (23*4^((s-1)/2) - 5)/3 - n, where r = ceiling(2*log_4((3n+4)/7)) and s = ceiling(2*log_4((3n+4)/8)).
%F A132668 a(n) = (4^floor(1 + (k+1)/2) + 7*4^floor(k/2) - 5)/3 - 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).
%F A132668 G.f.: g(x) = (x(1-2x)/(1-x) + 4x^2*f'(x^(7/3)) + (7/16)*(f'(x^(1/3)) - 4x - 1))/(1-x) where f(x) = Sum_{k>=0} x^(4^k) and f'(z) = derivative of f(x) at x = z.
%F A132668 a(n) = A133628(m) + A133628(m+1) + 1 - n, where m:=max{ k | A133628(k) <n }.
%F A132668 a(A133628(n) + 1) = A133628(n+1).
%F A132668 a(A133628(n)) = A133628(n-1) + 1 for n > 0.
%Y A132668 For formulas concerning a general parameter p (with respect to the recurrence rule ... a(n) = p*a(n-1) ...) see A132374.
%Y A132668 For p=2 to p=10 see A132666 through A132674.
%Y A132668 Cf. A133628.
%K A132668 nonn
%O A132668 1,2
%A A132668 _Hieronymus Fischer_, Aug 24 2007, Sep 15 2007, Sep 23 2007