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 A115384 Partial sums of Thue-Morse numbers A010060. 20
 0, 1, 2, 2, 3, 3, 3, 4, 5, 5, 5, 6, 6, 7, 8, 8, 9, 9, 9, 10, 10, 11, 12, 12, 12, 13, 14, 14, 15, 15, 15, 16, 17, 17, 17, 18, 18, 19, 20, 20, 20, 21, 22, 22, 23, 23, 23, 24, 24, 25, 26, 26, 27, 27, 27, 28, 29, 29, 29, 30, 30, 31, 32, 32, 33, 33, 33, 34, 34, 35, 36, 36, 36, 37, 38, 38 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS G. C. Greubel, Table of n, a(n) for n = 0..10000 FORMULA a(n) = Sum_{k=0..n} A010060(k)^2. a(n+1) = A115382(2n, n). a(n)/n -> 1/2; a(n) = number of odious numbers <= n, see A000069. - Reinhard Zumkeller, Aug 26 2007, corrected by M. F. Hasler, May 22 2017. a(n) = Sum_{i=1..n} (S2(n) mod 2), where S2 = binary weight; lim a(n)/n = 1/2. More generally, consider a(n) = Sum_{i=1..n} (F(Sk(n)) mod m), where Sk(n) is sum of digits of n, n in base k; F(t) is an arithmetic function; m integer. How does lim a(n)/n depend on F(t)? - Ctibor O. Zizka, Feb 25 2008 a(n) = n + 1 - A159481(n). - Reinhard Zumkeller, Apr 16 2009 a(n) = floor((n+1)/2)+(1+(-1)^n)*(1-(-1)^A000120(n))/4. - Vladimir Shevelev, May 27 2009 MATHEMATICA Accumulate[Nest[Flatten[#/.{0->{0, 1}, 1->{1, 0}}]&, {0}, 7]] (* Peter J. C. Moses, Apr 15 2013 *) Accumulate[ThueMorse[Range[0, 100]]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 02 2017 *) PROG (PARI) a(n)=(n+1)\2-(n%2&&hammingweight(n)%2) \\ Charles R Greathouse IV, Mar 22 2013 CROSSREFS Cf. A010060. Sequence in context: A125186 A226222 A140473 * A131411 A300068 A194202 Adjacent sequences:  A115381 A115382 A115383 * A115385 A115386 A115387 KEYWORD easy,nonn AUTHOR Paul Barry, Jan 21 2006 EXTENSIONS Edited by M. F. Hasler, May 22 2017 STATUS approved

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Last modified November 15 07:25 EST 2018. Contains 317225 sequences. (Running on oeis4.)