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A219660
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a(n) = number of bit-positions where Fibonacci numbers F(n) and F(n+1) contain both an 1-bit in their binary representation.
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2
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0, 1, 0, 1, 1, 0, 1, 2, 0, 2, 2, 1, 1, 4, 2, 3, 4, 3, 1, 4, 3, 1, 5, 4, 3, 3, 5, 7, 8, 4, 4, 3, 4, 8, 5, 4, 6, 6, 4, 7, 7, 10, 7, 11, 7, 8, 8, 4, 8, 12, 8, 9, 7, 8, 10, 13, 8, 8, 10, 8, 6, 12, 11, 12, 13, 10, 8, 7, 10, 13, 9, 9, 14, 12, 11, 9, 11, 13, 13, 13
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OFFSET
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0,8
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COMMENTS
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This sequence gives the number of "first-level" carries produced when computing Fibonacci numbers in binary arithmetic. that is, the carry-1-bits produced at the positions where the both summands F(n) and F(n+1) have 1-bits in the same bit-positions. This sum doesn't include any additional carries produced, when a produced carry-bit is added to an existing 1 at its left side.
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LINKS
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FORMULA
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EXAMPLE
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F_7 = 13, ......01101 in binary.
F_8 = 21, ......10101 in binary.
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Anded together: 00101
which has two 1-bits, thus a(7)=2.
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MATHEMATICA
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a[n_] := DigitCount[BitAnd[Fibonacci[n], Fibonacci[n+1]], 2, 1]; Array[a, 100, 0] (* Amiram Eldar, Jul 22 2023 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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