

A132666


a(1)=1, a(n) = 2*a(n1) if the minimal positive integer not yet in the sequence is greater than a(n1), else a(n) = a(n1)1.


23



1, 2, 4, 3, 6, 5, 10, 9, 8, 7, 14, 13, 12, 11, 22, 21, 20, 19, 18, 17, 16, 15, 30, 29, 28, 27, 26, 25, 24, 23, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85
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OFFSET

1,2


COMMENTS

Also: a(1)=1, a(n) = maximal positive number < a(n1) not yet in the sequence, if it exists, else a(n) = 2*a(n1).
Also: a(1)=1, a(n) = a(n1)1, if a(n1)  1 > 0 and has not been encountered so far, else a(n) = 2*a(n1).
A reordering of the natural numbers. The sequence is selfinverse in that a(a(n)) = n.
Almost certainly a duplicate of A132340.  R. J. Mathar, Jun 12 2008


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers


FORMULA

G.f.: g(x) = (x(12x)/(1x) + 2x^2*f'(x^3) + 3/4*(f'(x)2x1))/(1x) where f(x) = Sum_{k>=0} x^(2^k) and f'(z) = derivative of f(x) at x = z.
a(n) = 5*2^(r/2)  3  n, if both r and s are even, else a(n) = 7*2^((s1)/2)  3  n, where r = ceiling(2*log_2((n+2)/3)) and s = ceiling(2*log_2((n+2)/2)  1).
a(n) = 2^floor(1 + (k+1)/2) + 3*2^floor(k/2)  3  n, where k=r, if r is even, else k=s (with respect to r and s above; formally, k = ((r+s) + (rs)*(1)^r)/2).
a(n) = A027383(m) + A027383(m+1) + 1  n, where m:=max{ k  A027383(k) < n }.
a(A027383(n) + 1) = A027383(n+1).
a(A027383(n)) = A027383(n1) + 1 for n > 0.


MATHEMATICA

max = 72; f[x_] := Sum[x^(2^k), {k, 0, Ceiling[ Log[2, max]]}]; g[x_] = (x (1  2x)/(1  x) + 2x^2*f'[x^3] + 3/4*(f'[x]  2x  1))/(1  x); Drop[ CoefficientList[ Series[ g[x], {x, 0, max}], x], 1] (* JeanFrançois Alcover, Dec 01 2011 *)


PROG

(Haskell)
import Data.List (delete)
a132666 n = a132666_list !! (n1)
a132666_list = 1 : f 1 [2..] where
f z xs = y : f y (delete y xs) where
y  head xs > z = 2 * z
 otherwise = z  1
 Reinhard Zumkeller, Sep 17 2001


CROSSREFS

For formulas concerning a general parameter p (with respect to the recurrence rule ... a(n)=p*a(n1) ...) see A132674.
For p=3 to p=10 see A132667 through A132674.
For a similar recurrence rule concerning Fibonacci (A000045) and Lucas numbers (A000032) see A132664 and A132665.
Cf. A027383.
Sequence in context: A232642 A180625 A132340 * A116533 A087559 A193298
Adjacent sequences: A132663 A132664 A132665 * A132667 A132668 A132669


KEYWORD

nonn,nice


AUTHOR

Hieronymus Fischer, Aug 24 2007, Sep 15 2007


STATUS

approved



