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Bookmark or Share- Consecutive bit strings? - Mathematics Stack ExchangeThere are of course exactly as many that have exactly $9$ consecutive zeroes, and no $15$-bit string can have both, so there are $2\cdot144=288$ $15$-bit strings that contain exactly $9$ consecutive ones or consecutive zeroes.
- number theory - Can consecutive integers be perfect powers ...The fact that there exist finitely many was first proved by Tidjeman and a complete proof that $8=2^3$ and $9=3^2$ is the only pair of consecutive powers was proved by Preda Mihăilescu in 2002 and published in 2004. The proof is not an easy one to show here.
- Recurrence Relation for Bit String Length n with No Consecutive 0sBy the product rule, the number of bit-strings which surely have at least one pair of consecutive zeros is $(n-1) * 2^{n-2}$ It the product of possible choices for k and the number of bit-strings associated with each choice of k. Consequently, the number of bit-strings of length n with NO consecutive zeroes is. $2^n - (n-1)*2^{n-2}.$ Any comments!
- Some three consecutive numbers sum to at least $32$Here's a question we got for homework: We write down all the numbers from $1$ to $20$ in a circle. Prove that there is a sequence of $3$ numbers whose sum is at least $32$. I assume we need the
- Binary Sequences of length $n$ without $k$ consecutive $1$s or $0$sStack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
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