Alternating Groups that are Ambivalent

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Theorem

Let $n$ be a natural number.


Then the $n$th alternating group $A_n$ is ambivalent if and only if $n\in \{1, 2, 5, 6, 10, 14\}$.

This sequence is A115200 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Proof