This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A048679 Compressed fibbinary numbers (A003714), with rewrite 0->0, 01->1 applied to their binary expansion. 20
 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 Antti Karttunen, Table of n, a(n) for n = 0..10945 (terms 0..10000 from Alois P. Heinz) FORMULA 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 a(n) = A072650(A003714(n)) = A003188(A227351(n)). - Antti Karttunen, May 13 2018 MAPLE a(n) = rewrite_0to0_x1to1(fibbinary(j)) (where fibbinary(j) = A003714[ n ]) 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-François Alcover, Feb 27 2016, after Alois P. Heinz *) PROG (PARI) A072649(n) = { my(m); if(n<1, 0, m=0; until(fibonacci(m)>n, m++); m-2); }; \\ From A072649 A003714(n) = { my(s=0, w); while(n>2, w = A072649(n); s += 2^(w-1); n -= fibonacci(w+1)); (s+n); } A007814(n) = valuation(n, 2); A000265(n) = (n/2^valuation(n, 2)); A106151(n) = if(n<=1, n, if(n%2, 1+(2*A106151((n-1)/2)), (2^(A007814(n)-1))*A106151(A000265(n)))); A048679(n) = if(!n, n, A106151(2*A003714(n))); \\ Antti Karttunen, May 13 2018, after Reinhard Zumkeller's May 09 2005 formula. CROSSREFS Cf. A000045, A003714, A005203, A048678, A048680, A072650, A087808, A106151, A200714, A227351, A232559, A277006, A304100, A304101. Sequence in context: A054238 A225589 A245603 * A266412 A246365 A191729 Adjacent sequences:  A048676 A048677 A048678 * A048680 A048681 A048682 KEYWORD nonn,base AUTHOR 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 18 06:30 EDT 2018. Contains 313823 sequences. (Running on oeis4.)