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A048679
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Compressed fibbinary numbers (A003714), with rewrite 0->0, 01->1 applied to their binary expansion.
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22
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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
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OFFSET
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0,3
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COMMENTS
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Permutation of the nonnegative integers (A001477); inverse permutation of A048680 i.e. A048679[ A048680[ n ] ] = n for all n.
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 0..10945 (terms 0..10000 from Alois P. Heinz)
Index entries for sequences that are permutations of the natural numbers
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FORMULA
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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
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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.
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CROSSREFS
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Cf. A000045, A003714, A005203, A048678, A048680, A072650, A087808, A106151, A200714, A227351, A232559, A277006, A304100, A304101.
Sequence in context: A054238 A225589 A245603 * A342794 A266412 A246365
Adjacent sequences: A048676 A048677 A048678 * A048680 A048681 A048682
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KEYWORD
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nonn,base
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AUTHOR
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Antti Karttunen
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STATUS
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approved
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