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A059448
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If A_k are the terms from 2^(k-1) through to 2^k-1, then A_(k+1) is B_k A_k where B_k is A_k with 0's and 1's swapped, starting from a(1)=0; also parity of number of zero digits when n is written in binary.
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7
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0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(0) not given as it could be 1 or 0 depending on the definition or formula used.
The sequence (when prefixed by 0) is overlap-free [Allouche and Shallit].
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REFERENCES
| J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 26, Problem 23.
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LINKS
| Index entries for characteristic functions
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FORMULA
| a(2n)=1-a(n); a(2n+1)=a(n)=1-a(2n). If 2^k<=n<2^(k+1) then a(n)=1-a(n-2^(k-1)). a(n)=A023416(n) mod 2 =A059009(n)-2n =2n+1-A059010(n) =|A010060(n)-A030300(n-1)|.
Let b(1)=1 and b(n)=b(n-ceil(n/2))-b(n-floor(n/2)) then for n>=1 a(n)=(1/2)*(1-b(2n+1)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 26 2005
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MAPLE
| s1:=[];
for n from 1 to 200 do
t1:=convert(n, base, 2); t2:=subs(1=NULL, t1); s1:=[op(s1), nops(t2) mod 2]; od:
s1;
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PROG
| (PARI)
{a(n)=local(b=binary(n)); return( (sum(k=1, #b, 1-b[k])) % 2 ); }
vector(99, n, a(n)) /* show terms */
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CROSSREFS
| Characteristic function of A059009.
Sequence in context: A080846 A082401 A157238 * A156259 A138710 A179829
Adjacent sequences: A059445 A059446 A059447 * A059449 A059450 A059451
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KEYWORD
| nice,nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Feb 02 2001
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