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...
$\begingroup$
$\endgroup$
Add a comment
|
3 Answers
$\begingroup$
$\endgroup$
1
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, 2019 at 12:31
$\begingroup$
$\endgroup$
1
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).
Source-OEIS
-
2$\begingroup$ Note for the curious: this is in fact equivalent to JonMark Perry's answer. $\endgroup$– Gareth McCaughan ♦Mar 6, 2019 at 12:31
$\begingroup$
$\endgroup$
1
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, 2019 at 12:30