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A145037 Unreduced binary digital mean numerators, dm_num(2, n). 8
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; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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.

Also: number of 1's minus number of 0's in the binary representation of n. - M. F. Hasler, Mar 08 2018

LINKS

Table of n, a(n) for n=0..90.

FORMULA

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.

Let 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. - Reikku Kulon, Oct 02 2008

PROG

(Haskell)

a145037 0 = 0

a145037 n = a145037 n' + 2*m - 1 where (n', m) = divMod n 2

-- Reinhard Zumkeller, Jun 16 2011

(PARI) A145037(n)=hammingweight(n)*2-logint(n<<1+!n, 2) \\ M. F. Hasler, Mar 08 2018

CROSSREFS

Cf. A031443, A037861, A144912.

From Reikku Kulon, Oct 02 2008 or Oct 05 2008: (Start)

Cf. A000120, A001316, A006519, A002487.

Cf. A145057 (terms equal differences between n where a(n) equals zero).

Cf. A145058, A145059, A145060. (End)

Sequence in context: A077254 A074761 A037861 * A267115 A328919 A277647

Adjacent sequences:  A145034 A145035 A145036 * A145038 A145039 A145040

KEYWORD

base,easy,sign

AUTHOR

Reikku Kulon, Sep 30 2008

STATUS

approved

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Last modified February 20 04:12 EST 2020. Contains 332063 sequences. (Running on oeis4.)