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A345290
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a(n) is obtained by replacing 2^k in binary expansion of n with Fibonacci(-k-2).
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3
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0, -1, 2, 1, -3, -4, -1, -2, 5, 4, 7, 6, 2, 1, 4, 3, -8, -9, -6, -7, -11, -12, -9, -10, -3, -4, -1, -2, -6, -7, -4, -5, 13, 12, 15, 14, 10, 9, 12, 11, 18, 17, 20, 19, 15, 14, 17, 16, 5, 4, 7, 6, 2, 1, 4, 3, 10, 9, 12, 11, 7, 6, 9, 8, -21, -22, -19, -20, -24
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OFFSET
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0,3
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COMMENTS
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This sequence is a variant of A022290; here we consider Fibonacci numbers with negative indices (A039834), there Fibonacci numbers with positive indices (A000045).
After the initial 0, the sequence alternates runs of positive terms and runs of negative terms, the k-th run having 2^(k-1) terms.
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LINKS
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FORMULA
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a(n) = 0 iff n = 0.
a(n) = -1 iff n belongs to A020989.
a(n) = -2 iff n belongs to A136412.
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EXAMPLE
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For n = 3:
- 3 = 2^1 + 2^0,
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PROG
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(PARI) a(n) = { my (v=0, e); while (n, n-=2^e=valuation(n, 2); v+=fibonacci(-2-e)); v }
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CROSSREFS
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Cf. A000045, A000695, A020989, A022290, A039834, A062880, A063694, A063695, A072197, A080675, A136412, A345291, A345292.
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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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