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A036585
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Ternary Thue-Morse sequence: closed under a->abc, b->ac, c->b.
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9
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3, 2, 1, 3, 1, 2, 3, 2, 1, 2, 3, 1, 3, 2, 1, 3, 1, 2, 3, 1, 3, 2, 1, 2, 3, 2, 1, 3, 1, 2, 3, 2, 1, 2, 3, 1, 3, 2, 1, 2, 3, 2, 1, 3, 1, 2, 3, 1, 3, 2, 1, 3, 1, 2, 3, 2, 1, 2, 3, 1, 3, 2, 1, 3, 1, 2, 3, 1, 3, 2, 1, 2, 3, 2, 1, 3, 1, 2, 3, 1, 3, 2, 1, 3, 1, 2, 3, 2, 1, 2, 3, 1, 3, 2, 1, 2, 3, 2, 1, 3, 1, 2, 3, 2, 1
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OFFSET
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1,1
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COMMENTS
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First differences of A001969. Observed by Franklin T. Adams-Watters, proved by Max Alekseyev, Aug 30 2006
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REFERENCES
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M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, MA, 1983, p. 26.
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = A001969(n+1) - A001969(n). - Franklin T. Adams-Watters, Aug 28 2006
a(n) = A029883(n) + 2 = A036577(n) + 1.
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PROG
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(PARI) a(n)=if(n<1 || valuation(n, 2)%2, 2, 2-(-1)^subst(Pol(binary(n)), x, 1))
(Haskell)
a036585 n = a036585_list !! (n-1)
a036585_list = 3 : concat (map f a036585_list)
where f 1 = [1, 2, 3]; f 2 = [1, 3]; f 3 = [2]
-- Reinhard Zumkeller, Oct 31 2012
def A036585(n): return 2+(n.bit_count()&1)-((n-1).bit_count()&1) # Chai Wah Wu, Mar 03 2023
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CROSSREFS
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Cf. A001969, A007413, A005679.
Sequence in context: A237881 A112745 A205564 * A260454 A164848 A213514
Adjacent sequences: A036582 A036583 A036584 * A036586 A036587 A036588
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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