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

Author

Walt Rorie-Baety, Dec 07 2011

Keywords

• nonn
• base
• nice

Comments

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

Examples

			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.
		

Links

• Walt Rorie-Baety, Table of n, a(n) for n = 0..2500
• Project Euler, Problem 361: Subsequence of Thue-Morse sequence

Crossrefs

Cf. A010060, A063037.

Programs

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

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 *)

Extensions

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