A216195 - OEIS

A216195

Abelian complexity function of the period-doubling sequence (A096268).

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

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

OFFSET

1,1

REFERENCES

Michel Rigo, Formal Languages, Automata and Numeration Systems, 2 vols., Wiley, 2014. Mentions this sequence - see "List of Sequences" in Vol. 2.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Nathan Fox, Python code to generate sequence

FORMULA

a(1) = 2; a(2n) = a(n); a(4n-1) = a(n) + 1; a(4n+1) = a(n) + 1.

a(n) = A007302(n) + 1.

MATHEMATICA

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 *)

CROSSREFS

Cf. A007302, A096268.

Sequence in context: A070210 A100198 A164996 * A304333 A136510 A080071

Adjacent sequences: A216192 A216193 A216194 * A216196 A216197 A216198

KEYWORD

nonn,easy

AUTHOR

Nathan Fox, Mar 12 2013

STATUS

approved