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Search: id:A115384
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| 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; listen)
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OFFSET
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0,3
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COMMENT
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n/a(n)-->1/2; a(n) = number of odious numbers <= n, cf. A000069. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 26 2007
a(n) = n + 1 - A159481(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 16 2009]
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FORMULA
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a(n)=sum{k=0..n, A010060(k)^2}; a(n+1)=A115382(2n, n).
a(n) = sum_{i=1..n} S2(n) mod 2, where S@ = 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 (ctibor.zizka(AT)seznam.cz), Feb 25 2008
a(n)=floor((n+1)/2)+(1+(-1)^n)*(1-(-1)^A000120(n))/4. [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), May 27 2009]
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CROSSREFS
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Sequence in context: A055037 A125186 A140473 this_sequence A131411 A125059 A029112
Adjacent sequences: A115381 A115382 A115383 this_sequence A115385 A115386 A115387
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Jan 21 2006
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