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A216195
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Abelian complexity function of the period-doubling sequence (A096268).
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1
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2, 2, 3, 2, 3, 3, 3, 2, 3, 3, 4, 3, 4, 3, 3, 2, 3, 3, 4, 3, 4, 4, 4, 3, 4, 4, 4, 3, 4, 3, 3, 2, 3, 3, 4, 3, 4, 4, 4, 3, 4, 4, 5, 4, 5, 4, 4, 3, 4, 4, 5, 4, 5, 4, 4, 3, 4, 4, 4, 3, 4, 3, 3, 2, 3, 3, 4, 3, 4, 4, 4, 3, 4, 4, 5, 4, 5, 4, 4, 3, 4, 4, 5, 4, 5, 5, 5, 4, 5, 5, 5, 4, 5, 4, 4, 3, 4, 4, 5
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OFFSET
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1,1
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REFERENCES
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Michel Rigo, Formal Languages, Automata and Numeration Systems, 2 vols., Wiley, 2014. Mentions this sequence - see "List of Sequences" in Vol. 2.
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LINKS
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FORMULA
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a(1) = 2; a(2n) = a(n); a(4n-1) = a(n) + 1; a(4n+1) = a(n) + 1.
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MATHEMATICA
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a[n_]:=Count[BitXor[b1=IntegerDigits[n, 2]; b3=IntegerDigits[3*n, 2]; PadLeft[b1, Length[b3]], b3], 1]; Table[a[n] + 1, {n, 1, 100}] (* Vincenzo Librandi, Jan 13 2017 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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