Problem 346

Strong Repunits

The number 7 is special, because 7 is 111 written in base 2, and 11 written in base 6

(i.e. 7_{10} = 11_{6} = 111_{2}). In other words, 7 is a repunit in at least two bases b > 1.

We shall call a positive integer with this property a strong repunit. It
can be verified that there are 8 strong repunits below 50:
{1,7,13,15,21,31,40,43}.

Furthermore, the sum of all strong repunits below 1000 equals 15864.

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