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A356327
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Replace 2^k in binary expansion of n with A039834(1+k).
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5
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0, 1, -1, 0, 2, 3, 1, 2, -3, -2, -4, -3, -1, 0, -2, -1, 5, 6, 4, 5, 7, 8, 6, 7, 2, 3, 1, 2, 4, 5, 3, 4, -8, -7, -9, -8, -6, -5, -7, -6, -11, -10, -12, -11, -9, -8, -10, -9, -3, -2, -4, -3, -1, 0, -2, -1, -6, -5, -7, -6, -4, -3, -5, -4, 13, 14, 12, 13, 15, 16
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OFFSET
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0,5
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COMMENTS
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This sequence has similarities with A022290, and is related to negaFibonacci representations.
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LINKS
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FORMULA
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Empirically:
- a(n) = 0 iff n = 0 or n belongs to A072197,
- a(n) = 1 iff n belongs to A020989,
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EXAMPLE
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For n = 13:
- 13 = 2^3 + 2^2 + 2^0,
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MATHEMATICA
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Table[Reverse[#].Fibonacci[-Range[Length[#]]] &@ IntegerDigits[n, 2], {n, 0, 69}] (* Rémy Sigrist, Aug 05 2022 *)
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PROG
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(PARI) a(n) = { my (v=0, k); while (n, n-=2^k=valuation(n, 2); v+=fibonacci(-1-k)); return (v) }
(Python)
from sympy import fibonacci
def A356327(n): return sum(fibonacci(-a)*int(b) for a, b in enumerate(bin(n)[:1:-1], start=1)) # Chai Wah Wu, Aug 31 2022
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CROSSREFS
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Cf. A000201, A001950, A003714, A004957, A020989, A022290, A026351, A039834, A060144, A072197, A189663, A215024, A215025, A309076, A356325, A356326.
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KEYWORD
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sign,base
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AUTHOR
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STATUS
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approved
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