A036585 - OEIS

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A036585

Ternary Thue-Morse sequence: closed under a->abc, b->ac, c->b.

9

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

First differences of A001969. Observed by Franklin T. Adams-Watters, proved by Max Alekseyev, Aug 30 2006

REFERENCES

M. Lothaire, Combinatorics on Words. Addison-Wesley, Reading, MA, 1983, p. 26.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A001969(n+1) - A001969(n). - Franklin T. Adams-Watters, Aug 28 2006

a(n) = A029883(n) + 2 = A036577(n) + 1.

MATHEMATICA

Differences[ThueMorse[Range[0, 100]]] + 2 (* Paolo Xausa, Oct 25 2024 *)

PROG

(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

(Python)

def A036585(n): return 2+(n.bit_count()&1)-((n-1).bit_count()&1) # Chai Wah Wu, Mar 03 2023

CROSSREFS

Cf. A001969, A007413, A005679.

Sequence in context: A237881 A112745 A205564 * A260454 A164848 A213514

Adjacent sequences: A036582 A036583 A036584 * A036586 A036587 A036588

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved