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A022290
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Replace 2^k in binary expansion of n by k-th Fibonacci number.
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8
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0, 1, 2, 3, 3, 4, 5, 6, 5, 6, 7, 8, 8, 9, 10, 11, 8, 9, 10, 11, 11, 12, 13, 14, 13, 14, 15, 16, 16, 17, 18, 19, 13, 14, 15, 16, 16, 17, 18, 19, 18, 19, 20, 21, 21, 22, 23, 24, 21, 22, 23, 24, 24, 25, 26, 27, 26, 27, 28, 29, 29, 30, 31, 32, 21, 22, 23, 24, 24, 25, 26
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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_Reinhard Zumkeller_, Table of n, a(n) for n = 0..10000
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FORMULA
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G.f.: 1/(1-x) * sum[k>=0, F(k+2)*x^2^k/(1+x^2^k)], F(n)=A000045(n).
a(n) = Sum_k>=0 {A030308(n,k)*A000045(k+2)}. - Philippe Deléham, Oct 15 2011
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MATHEMATICA
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Table[Reverse[#].Fibonacci[1 + Range[Length[#]]] &@ IntegerDigits[n, 2], {n, 0, 54}] (* IWABUCHI Yu(u)ki, Aug 01 2012 *)
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PROG
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(Haskell)
a022290 0 = 0
a022290 n = h n 0 $ drop 2 a000045_list where
h 0 y _ = y
h x y (f:fs) = h x' (y + f * r) fs where (x', r) = divMod x 2
-- Reinhard Zumkeller, Oct 03 2012
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CROSSREFS
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Other sequences that are built by replacing 2^k in the binary representation with other numbers: A029931 (naturals), A059590 (factorials), A089625 (primes).
Sequence in context: A203899 A202704 A029931 * A185363 A103827 A094182
Adjacent sequences: A022287 A022288 A022289 * A022291 A022292 A022293
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KEYWORD
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nonn
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AUTHOR
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Marc LeBrun
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STATUS
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approved
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