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Old 2008-06-19, 21:33   #1
davar55
 
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May 2004
New York City

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Default Shift Equivalency

Consider the set of B^N N-digit numbers in base B, with lead zeros
being significant. Call two such numbers "shift-equivalent" if one can
be mapped to the other by a rotation or a reversal of a rotation.
This partitions the set into equivalence classes, each of which can
contain at most 2N elements.

For example, with B=10 and N=4, these are some equivalence classes:

{1357,3571,5713,7135,7531,5317,3175,1753},
{1111},
{1122,1221,2211,2112},
{1313,3131}

For B=N=10, two problems:

Compute the number of equivlence classes.
Exhibit an equivalence class with a maximal number of primes.
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