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A076826 a(n) = 2*(Sum_{k=0..n} A010060(k)) - n, where A010060 is a Thue-Morse sequence. 6
0, 1, 2, 1, 2, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 1, 2, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 1, 2, 1, 0, 1, 0, 1, 2, 1, 2, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 1, 2, 1, 0, 1, 0, 1, 2, 1, 2, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 2, 1, 2, 1, 0, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Is there any interesting sequence b(n) such that b(n) mod 3 = a(n)?

Fixed point of the morphism 0->012; 1->1; 2->210 starting with a(0) = 0. - Philippe Deléham, Mar 14 2004

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..8191

Index entries for sequences that are fixed points of mappings

FORMULA

a(2k+1) = 1, a(4k) = (2k), a(4k+2) = 2-a(2k). - Michael Somos, Dec 04 2002

a(2n) = 2*A010060(n); a(2n+1) = 1. - Benoit Cloitre, Mar 08 2004

a(n) = 2*(A026430(n+1) - 1) mod 3. - Philippe Deléham, Mar 28 2004

a(n) = (number of odious numbers <= n) - (number of evil numbers <= n) for n>0. - T. D. Noe, Jun 14 2007

a(n) = 2*A115384(n) - n. - Vladimir Shevelev, May 31 2009

a(n) = 0 if n and A000120(n) are even; a(n) = 2 if n is even but A000120(n) is odd; a(n) = 1 if n is odd. - Vladimir Shevelev, May 31 2009

MATHEMATICA

Nest[ Function[ l, {Flatten[(l /. {0 -> {0, 1, 2}, 1 -> {1}, 2 -> {2, 1, 0}}) ]}], {0}, 6] (* Robert G. Wilson v, Mar 03 2005 *)

cnt=0; Join[{0}, Table[If[EvenQ[Count[IntegerDigits[n, 2], 1]], cnt--, cnt++ ]; cnt, {n, 150}]] (* T. D. Noe, Jun 14 2007 *)

PROG

(PARI) a(n)=if(n<0, 0, 2*sum(k=1, n, subst(Pol(binary(k)), x, 1)%2)-n)

(PARI) a(n)=if(n<1, 0, if(n%2, 1, if(n/2%2, 2-a(n\4*2), a(n/2))))

CROSSREFS

Cf. A000069 (odious numbers), A001969 (evil numbers).

Cf. A000120, A007413, A010060, A026430, A115384, A159481.

Sequence in context: A276469 A272356 A102565 * A137178 A101666 A035224

Adjacent sequences:  A076823 A076824 A076825 * A076827 A076828 A076829

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Nov 24 2002

STATUS

approved

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Last modified October 17 10:50 EDT 2017. Contains 293469 sequences.