A201992 Numbers whose binary representations are found in the Thue-Morse sequence.

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

Offset

0,3

Comments

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

Links

Walt Rorie-Baety, Table of n, a(n) for n = 0..2500

Project Euler, Problem 361: Subsequence of Thue-Morse 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 (n-1)) . map (take n) .  tails; binRep = foldl' (\a b -> 2*a+b) 0}; full = not . null

Crossrefs

Cf. A010060, A063037.

Sequence in context: A286262 A330029 A368841 * A329297 A236562 A157189

Adjacent sequences: A201989 A201990 A201991 * A201993 A201994 A201995

Keyword

nonn,base,nice

Author

Walt Rorie-Baety, Dec 07 2011

Extensions

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

Status

approved