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A095190 Doubled Thue-Morse sequence: the A010060 sequence replacing 0 by 0,0 and 1 by 1,1. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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.

REFERENCES

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

LINKS

Table of n, a(n) for n=0..104.

FORMULA

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

EXAMPLE

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 ...

PROG

(PARI) a(n)=hammingweight(n\2)%2 \\ Charles R Greathouse IV, May 08 2016

CROSSREFS

Cf. A010059, A010060, A096288, A096289.

Sequence in context: A011657 A072126 A111113 * A131735 A131736 A152228

Adjacent sequences:  A095187 A095188 A095189 * A095191 A095192 A095193

KEYWORD

easy,nonn

AUTHOR

Miklos Kristof and Peter Boros, Jun 21 2004

STATUS

approved

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Last modified December 6 12:54 EST 2016. Contains 278781 sequences.