sentences:  The term economical number has been used about a frugal number, but also about a number which is either frugal or equidigital.Let formula_1 be a number base, and let formula_2 be the number of digits in a natural number formula_3 for base formula_4.A natural number formula_3 has the integer factorisation
  and is an frugal number in base formula_4 if
  where formula_9 is the p-adic valuation of formula_3.