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A368595
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Alternating sum of A006519.
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1
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-1, 1, 0, 4, 3, 5, 4, 12, 11, 13, 12, 16, 15, 17, 16, 32, 31, 33, 32, 36, 35, 37, 36, 44, 43, 45, 44, 48, 47, 49, 48, 80, 79, 81, 80, 84, 83, 85, 84, 92, 91, 93, 92, 96, 95, 97, 96, 112, 111, 113, 112, 116, 115, 117, 116, 124, 123, 125, 124, 128, 127, 129, 128
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OFFSET
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1,4
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COMMENTS
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a(n) <= (n/2)*log_2 n, with equality at powers of 2.
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LINKS
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FORMULA
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a(n) = Sum_{i=1..n} (-1)^i*A006519(i).
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MATHEMATICA
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a[1]=-1; a[n_]:=If[OddQ[n], a[n-1]-2^IntegerExponent[n, 2], a[n-1]+2^IntegerExponent[n, 2]]; Table[a[n], {n, 63}] (* James C. McMahon, Dec 31 2023 *)
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PROG
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(PARI) a(n) = fromdigits(Vec(Pol(binary(n))'), 2) - bitand(n, 1); \\ Kevin Ryde, Jan 01 2024
(Python)
def A368595(n): return sum(map(lambda x:(x[0]+1)*(1<<x[0]), filter(lambda x:x[1]=='1', enumerate(bin(n)[-2:1:-1]))))-(n&1) # Chai Wah Wu, Jan 01 2024
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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