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A132670 a(1)=1, a(n) = 6*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 A132670 #8 Aug 09 2017 23:07:39
%S A132670 1,6,5,4,3,2,12,11,10,9,8,7,42,41,40,39,38,37,36,35,34,33,32,31,30,29,
%T A132670 28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,78,77,76,75,74,73,72,
%U A132670 71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49
%N A132670 a(1)=1, a(n) = 6*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 A132670 Also: a(1)=1, a(n) = maximal positive integer < a(n-1) not yet in the sequence, if it exists, else a(n) = 6*a(n-1).
%C A132670 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) = 6*a(n-1).
%C A132670 A permutation of the positive integers. The sequence is self-inverse, in that a(a(n)) = n.
%F A132670 G.f.: g(x) = (x(1-2x)/(1-x) + 6x^2*f'(x^(11/5)) + (11/36)*(f'(x^(1/5)) - 6x - 1)/(1-x) where f(x) = Sum_{k>=0} x^(6^k) and f'(z) = derivative of f(x) at x = z.
%F A132670 a(n) = (17*6^(r/2) - 7)/5 - n if both r and s are even, else a(n) = (47*6^((s-1)/2) - 7)/5 - n, where r = ceiling(2*log_6((5n+6)/11)) and s = ceiling(2*log_6((5n+6)/6)) - 1.
%F A132670 a(n) = (6^floor(1 + (k+1)/2) + 11*6^floor(k/2) - 7)/5 - 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 A132670 For formulas concerning a general parameter p (with respect to the recurrence rule ... a(n)=p*a(n-1) ...) see A132374.
%Y A132670 For p=2 to p=10 see A132666 through A132674.
%K A132670 nonn
%O A132670 1,2
%A A132670 _Hieronymus Fischer_, Sep 15 2007