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A201992 Numbers whose binary representations are found in the Thue-Morse 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 (list; graph; refs; listen; history; text; internal format)
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: A023776 A063037 A286262 * A236562 A157189 A136250

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

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Last modified March 22 10:07 EDT 2019. Contains 321421 sequences. (Running on oeis4.)