

A201992


Numbers whose binary representations are found in the ThueMorse sequence.


1



0, 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 13, 18, 19, 20, 22, 25, 26, 37, 38, 41, 44, 45, 50, 51, 52, 75, 76, 77, 82, 83, 89, 90, 101, 102, 105, 150, 153, 154, 165, 166, 179, 180, 203, 205, 210, 211, 300, 301, 306, 308, 331, 332, 358, 361, 406, 410, 421, 422, 601
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OFFSET

0,3


COMMENTS

Interpreting A010060 as a bit string, this sequence contains the decimal equivalents of the subsequences, in order.


LINKS

Walt RorieBaety, Table of n, a(n) for n = 0..2500
Project Euler, Problem 361: Subsequence of ThueMorse sequence


EXAMPLE

The binary representation of 21 (10101) has an overlapping square sequence (1X1X1, where X is any binary sequence, in this case, X = 0), and so is not in the sequence. Compare to A063037.


MATHEMATICA

Module[{nn=10000, tm}, tm=Table[ThueMorse[n], {n, 0, nn}]; Join[{0}, Position[ Table[ If[SequenceCount[tm, IntegerDigits[k, 2]]>0, 1, 0], {k, 1000}], 1]]]// Flatten (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 03 2018 *)


PROG

(Haskell) a201992 = 0: concatMap (\n > Set.toList . Set.fromList . map binRep . filter ((==[1]).take 1) . window n . take (n*2^n) $ a010060) [1..] where
{window n = takeWhile (full . drop (n1)) . map (take n) . tails; binRep = foldl' (\a b > 2*a+b) 0}; full = not . null


CROSSREFS

Cf. A010060, A063037.
Sequence in context: A023776 A063037 A286262 * A236562 A157189 A136250
Adjacent sequences: A201989 A201990 A201991 * A201993 A201994 A201995


KEYWORD

nonn,base,nice


AUTHOR

Walt RorieBaety, Dec 07 2011


EXTENSIONS

Helper function added and name of value in program changed for better understanding by Walt RorieBaety, Mar 25 2012


STATUS

approved



