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A048679 Compressed fibbinary numbers (A003714), with rewrite 0->0, 01->1. 17
0, 1, 2, 4, 3, 8, 5, 6, 16, 9, 10, 12, 7, 32, 17, 18, 20, 11, 24, 13, 14, 64, 33, 34, 36, 19, 40, 21, 22, 48, 25, 26, 28, 15, 128, 65, 66, 68, 35, 72, 37, 38, 80, 41, 42, 44, 23, 96, 49, 50, 52, 27, 56, 29, 30, 256, 129, 130, 132, 67, 136, 69, 70, 144, 73, 74, 76, 39, 160, 81 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Permutation of the nonnegative integers (A001477); inverse permutation of A048680 i.e. A048679[ A048680[ n ] ] = n for all n.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(n) = rewrite_0to0_x1to1(fibbinary(j)) (where fibbinary(j) = A003714[ n ])

a(n) = A106151(2*A003714(n)) for n > 0. - Reinhard Zumkeller, May 09 2005

a(n+1) = min{([a(n)/2]+1)*2^k} such that it is not yet in the sequence. - Gerard Orriols, Jun 07 2014

MAPLE

rewrite_0to0_x1to1 := proc(n) option remember; if(0 = n) then RETURN(n); else RETURN((2 * rewrite_0to0_x1to1(floor(n/(2^(1+(n mod 2)))))) + (n mod 2)); fi; end;

fastfib := n -> round((((sqrt(5)+1)/2)^n)/sqrt(5)); fibinv_appr := n -> floor(log[ (sqrt(5)+1)/2 ](sqrt(5)*n)); fibinv := n -> (fibinv_appr(n) + floor(n/fastfib(1+fibinv_appr(n)))); fibbinary := proc(n) option remember; if(n <= 2) then RETURN(n); else RETURN((2^(fibinv(n)-2))+fibbinary_seq(n-fastfib(fibinv(n)))); fi; end;

# second Maple program:

b:= proc(n) is(n=0) end:

a:= proc(n) option remember; local h; h:= iquo(a(n-1), 2)+1;

      while b(h) do h:= h*2 od; b(h):=true; h

    end: a(0):=0:

seq(a(n), n=0..100);  # Alois P. Heinz, Sep 22 2014

MATHEMATICA

b[n_] := n==0; a[n_] := a[n] = Module[{h}, h = Quotient[a[n-1], 2] + 1; While[b[h], h = h*2]; b[h] = True; h]; a[0]=0; Table[a[n], {n, 0, 100}] (* Jean-Fran├žois Alcover, Feb 27 2016, after Alois P. Heinz *)

CROSSREFS

Cf. A003714, A005203, A048678, A048680.

Sequence in context: A054238 A225589 A245603 * A266412 A246365 A191729

Adjacent sequences:  A048676 A048677 A048678 * A048680 A048681 A048682

KEYWORD

nonn

AUTHOR

Antti Karttunen

STATUS

approved

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Last modified February 25 10:54 EST 2018. Contains 299653 sequences. (Running on oeis4.)