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%I #19 Mar 03 2023 16:25:48
%S 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,
%T 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,
%U 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
%N Ternary Thue-Morse sequence: closed under a->abc, b->ac, c->b.
%C First differences of A001969. Observed by Franklin T. Adams-Watters, proved by Max Alekseyev, Aug 30 2006
%D M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, MA, 1983, p. 26.
%H Reinhard Zumkeller, <a href="/A036585/b036585.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A001969(n+1) - A001969(n). - _Franklin T. Adams-Watters_, Aug 28 2006
%F a(n) = A029883(n) + 2 = A036577(n) + 1.
%o (PARI) a(n)=if(n<1 || valuation(n,2)%2,2,2-(-1)^subst(Pol(binary(n)),x,1))
%o (Haskell)
%o a036585 n = a036585_list !! (n-1)
%o a036585_list = 3 : concat (map f a036585_list)
%o where f 1 = [1,2,3]; f 2 = [1,3]; f 3 = [2]
%o -- _Reinhard Zumkeller_, Oct 31 2012
%o def A036585(n): return 2+(n.bit_count()&1)-((n-1).bit_count()&1) # _Chai Wah Wu_, Mar 03 2023
%Y Cf. A001969, A007413, A005679.
%K nonn
%O 1,1
%A _N. J. A. Sloane_.
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