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Search: id:A145037
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| A145037 |
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Unreduced binary digital mean numerators, dm_num(2, n). |
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+0
3
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| 0, 1, 0, 2, -1, 1, 1, 3, -2, 0, 0, 2, 0, 2, 2, 4, -3, -1, -1, 1, -1, 1, 1, 3, -1, 1, 1, 3, 1, 3, 3, 5, -4, -2, -2, 0, -2, 0, 0, 2, -2, 0, 0, 2, 0, 2, 2, 4, -2, 0, 0, 2, 0, 2, 2, 4, 0, 2, 2, 4, 2, 4, 4, 6, -5, -3, -3, -1, -3, -1, -1, 1, -3, -1, -1, 1, -1, 1, 1, 3, -3, -1, -1, 1, -1, 1, 1, 3, -1, 1, 1
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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The first column of A144912 begins at n = 2. Zeros in that column correspond to A031443.
Compare A037861, which is the negative of this sequence beginning at n = 1.
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FORMULA
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dm_num(2, n) = sigma(i in [1, d]: d_i * 2 - 1), where d is the number of digits in the binary representation of n and d_i the individual digits.
Contribution from Reikku Kulon (reikku(AT)gmail.com), Oct 02 2008: (Start)
Define f(n) = A000120(n) = log2[A001316(n)] = log2[2 * A001316(n - 1) / A006519(n)].
Then a(n) = a(n - 1) + 2 * (f(n) - f(n - 1)), subtracted by 1 if f(n) equals 1.
Note that A006519(n) can be expressed simply in two's complement representation as bitwise-and(+n, -n) or more generally as bitwise-and(n, 1 + bitwise-not(n)). (End)
A006519(n) can also be defined as 2^floor(A002487(n - 1) / A002487(n)). [From Reikku Kulon (reikku(AT)gmail.com), Oct 05 2008]
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CROSSREFS
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Cf. A031443, A037861, A144912
Contribution from Reikku Kulon (reikku(AT)gmail.com), Oct 02 2008: (Start)
Cf. A000120, A001316, A006519
Cf. A145057 (terms equal differences between n where a(n) equals zero)
Cf. A145058, A145059, A145060 (End)
Cf. A002487 [From Reikku Kulon (reikku(AT)gmail.com), Oct 05 2008]
Sequence in context: A077254 A074761 A037861 this_sequence A158052 A158378 A052409
Adjacent sequences: A145034 A145035 A145036 this_sequence A145038 A145039 A145040
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KEYWORD
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base,easy,sign
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AUTHOR
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Reikku Kulon (reikku(AT)gmail.com), Sep 30 2008
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