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Problem
Answer published by the source. Consult the official source to check your work against its answer.
question
A Skolem sequence of order is a sequence of integers satisfying the conditions:
i) for every in , there exist exactly two elements and with , and
ii) if with , then .
For example, is a Skolem sequence of order 4.
List all Skolem sequences of order 4.
Plain-text mathematical notation (without MathML)
A Skolem sequence of order n is a sequence (s₁,s₂,…,s_(2n)) of 2n integers satisfying the conditions:
i) for every k in {1,2,3,…,n}, there exist exactly two elements s_(i) and s_(j) with s_(i)=s_(j)=k, and
ii) if s_(i)=s_(j)=k with i<j, then j−i=k.
For example, (4,2,3,2,4,3,1,1) is a Skolem sequence of order 4.
List all Skolem sequences of order 4.Original LaTeX notation
A Skolem sequence of order $n$ is a sequence $\left(s_{1}, s_{2}, \ldots, s_{2 n}\right)$ of $2 n$ integers satisfying the conditions:
i) for every $k$ in $\{1,2,3, \ldots, n\}$, there exist exactly two elements $s_{i}$ and $s_{j}$ with $s_{i}=s_{j}=k$, and
ii) if $s_{i}=s_{j}=k$ with $i<j$, then $j-i=k$.
For example, $(4,2,3,2,4,3,1,1)$ is a Skolem sequence of order 4.
List all Skolem sequences of order 4.answer type
Tuple
is multiple answer
true
language
English
question type
Open-ended
subject
Math
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