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A132673 a(1)=1, a(n) = 9*a(n-1) if the minimal positive integer number not yet in the sequence is greater than a(n-1), else a(n) = a(n-1) - 1.

%I A132673 #11 Aug 09 2017 23:07:40
%S A132673 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,
%T A132673 82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,
%U A132673 59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37
%N A132673 a(1)=1, a(n) = 9*a(n-1) if the minimal positive integer number not yet in the sequence is greater than a(n-1), else a(n) = a(n-1) - 1.
%C A132673 Also: a(1)=1, a(n) = maximal positive number < a(n-1) not yet in the sequence, if it exists, else a(n) = 9*a(n-1).
%C A132673 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).
%C A132673 A permutation of the positive integers. The sequence is self-inverse, in that a(a(n)) = n.
%F A132673 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.
%F A132673 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.
%F A132673 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).
%Y A132673 For formulas concerning a general parameter p (with respect to the recurrence rule ... a(n) = p*a(n-1) ...) see A132374.
%Y A132673 For p=2 to p=10 see A132666 through A132674.
%K A132673 nonn
%O A132673 1,2
%A A132673 _Hieronymus Fischer_, Sep 15 2007