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A095190
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Doubled Thue-Morse sequence: the A010060 sequence replacing 0 by 0,0 and 1 by 1,1.
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7
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0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1
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OFFSET
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0,1
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COMMENTS
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If b(n)=A010060, then a(2n)=b(n), a(2n+1)=b(n).
Let n=Sum(c(k)*2^k), c(k)=0,1, be the binary form of n, n=Sum(d(k)*3^k), d(k)=0,1,2, the ternary form, n=Sum(e(k)*5^k), e(k)=0,1,2,3,4, the base 5 form. Then a(n)=Sum(c(k)+d(k)) mod 2 = Sum(c(k)+e(k)) mod 2.
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REFERENCES
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Mignosi, F.; Restivo, A.; Sciortino, M. Words and forbidden factors. WORDS (Rouen, 1999). Theoret. Comput. Sci. 273 (2002), no. 1-2, 99--117. MR1872445 (2002m:68096) - From N. J. A. Sloane, Jul 10 2012
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LINKS
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Table of n, a(n) for n=0..104.
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FORMULA
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a(n) = A096273(n) mod 2 - Benoit Cloitre, Jun 29 2004
a(n)=mod(A000120(floor(n/2)), 2)=mod(A010060(floor(n/2)), 2). - Paul Barry, Jan 07 2005
a(n)=mod(-1+sum{k=0..n, mod(C(n, 2k), 2)}, 3); - Paul Barry, Jan 14 2005
a(n)=mod(log_2(sum{k=0..n, mod(C(n,2k),2)}),2); - Paul Barry, Jun 12 2006
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EXAMPLE
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The Thue-Morse sequence is: 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 ... so a(n) = 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 ...
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CROSSREFS
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Cf. A010059, A010060, A096288, A096289.
Sequence in context: A011657 A072126 A111113 * A131735 A131736 A152228
Adjacent sequences: A095187 A095188 A095189 * A095191 A095192 A095193
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KEYWORD
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easy,nonn
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AUTHOR
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Miklos Kristof and Peter Boros (kristmikl(AT)freemail.hu), Jun 21 2004
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STATUS
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approved
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