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math.HO2019

Prime-bounded subwords

Onno M. Cain

In the number $373$ all subwords ( $3$ , $7$ , $37$ , $73$ , and $373$ ) are prime. Similarly, in $9719$ all subwords are divisible by at most one prime. And similarly again in $73197979…

math.HO2019

The Exceptional Selfcondensability of Powers of Five

O. M. Cain

We show any power of five may be expressed arithmetically with the digits of its decimal representation. We also show powers of five (in decimal) contain any amount of zeros in a r…