One friend has given me this binary sequence and asked what is its speciality if we add next few terms to this sequence?
The binary sequence was: $$\color{blue}{\underline{100101100110100}}101101001 \dots$$ Hints Given: It's a Classical one.
So,could anyone please help me to recognise its speciality...


Is it:

The (opposite of the) Thue-Morse sequence.

Start with $1 \to 10 \to 1001 \to 10010110 \to 1001011001101001$, where at each step the opposite of what is already there is added.

  • 1
    $\begingroup$ Note for the curious: this is in fact equivalent to gopal's answer. $\endgroup$ – Gareth McCaughan Mar 6 '19 at 12:31

It could be

Binary strings that have 1s where 'evil numbers' occur, 0s elsewhere and every term ends >!with the n-th evil number index (counting with 0 = first).


  • 2
    $\begingroup$ Note for the curious: this is in fact equivalent to JonMark Perry's answer. $\endgroup$ – Gareth McCaughan Mar 6 '19 at 12:31

It could be:

Morse code with a 1 as a dot, a 11 as a dash, 0 as a gap between dots and dashes, and 00 as gap between letters.

In which case:

The message becomes "EANRE". Not sure if this is if any note...

  • 1
    $\begingroup$ Curiously, Morse is relevant here, but not that Morse. $\endgroup$ – Gareth McCaughan Mar 6 '19 at 12:30

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