A132672 a(1)=1, a(n) = 8*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.

1, 8, 7, 6, 5, 4, 3, 2, 16, 15, 14, 13, 12, 11, 10, 9, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17

Offset: 1

Author

Hieronymus Fischer, Sep 15 2007

Keywords

• nonn

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.

Crossrefs

For formulas concerning a general parameter p (with respect to the recurrence rule ... a(n)=p*a(n-1) ...) see A132374.

For p=2 to p=10 see A132666 through A132674.

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).