This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A132666 a(1)=1, a(n) = 2*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. 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also: a(1)=1, a(n) = maximal positive number < a(n-1) not yet in the sequence, if it exists, else a(n) = 2*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) = 2*a(n-1). A reordering of the natural numbers. The sequence is self-inverse 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 FORMULA G.f.: g(x) = (x(1-2x)/(1-x) + 2x^2*f'(x^3) + 3/4*(f'(x)-2x-1))/(1-x) 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^((s-1)/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) + (r-s)*(-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(n-1) + 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] (* Jean-François Alcover, Dec 01 2011 *) PROG (Haskell) import Data.List (delete) a132666 n = a132666_list !! (n-1) 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(n-1) ...) 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 18 18:56 EDT 2019. Contains 328197 sequences. (Running on oeis4.)