OFFSET
1,2
COMMENTS
Also: a(1)=1, a(n) = maximal positive integer < a(n-1) not yet in the sequence, if it exists, else a(n) = 8*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) = 8*a(n-1).
A permutation of the positive integers. The sequence is self-inverse, in that a(a(n)) = n.
FORMULA
G.f.: g(x) = (x(1-2x)/(1-x) + 8x^2*f'(x^(15/7)) + (15/64)*(f'(x^(1/7)) - 8x-1)/(1-x) where f(x) = Sum_{k>=0} x^(8^k) and f'(z) = derivative of f(x) at x = z.
a(n) = (23*8^(r/2) - 9)/7 - n if both r and s are even, else a(n) = (78*8^((s-1)/2) - 9)/7 - n, where r = ceiling(2*log_8((7n+8)/15)) and s = ceiling(2*log_8(7n+8)/7)) - 1.
a(n) = (8^floor(1 + (k+1)/2) + 15*8^floor(k/2) - 9)/7 - 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).
CROSSREFS
For formulas concerning a general parameter p (with respect to the recurrence rule ... a(n)=p*a(n-1) ...) see A132374.
KEYWORD
nonn
AUTHOR
Hieronymus Fischer, Sep 15 2007
STATUS
approved