Frugal number

In number theory, a frugal number is a natural number in a given number base that has more digits than the number of digits in its prime factorization in the given number base (including exponents).[1] For example, in base 10, 125 = 53, 128 = 27, 243 = 35, and 256 = 28 are frugal numbers (sequence A046759 in the OEIS), and in base 2, thirty-two is a frugal number, since 100000 = 10101.

The term economical number has been used about a frugal number, but also about a number which is either frugal or equidigital.

Mathematical definition

Let be a number base, and let be the number of digits in a natural number for base . A natural number has the integer factorisation

and is an frugal number in base if

where is the p-adic valuation of .

gollark: JEI = NEI = PotatOS
gollark: The best way to do it is probably "check first characters match, check lengths match".
gollark: Ah, good, it is not.
gollark: If it *is* O(n) I'll just use a simpler heuristic, like "first character of strings match".
gollark: This is Cobalt, I bet the lua strings are just java byte arrays.

See also

Notes

  1. Darling, David J. (2004). The universal book of mathematics: from Abracadabra to Zeno's paradoxes. John Wiley & Sons. p. 102. ISBN 978-0-471-27047-8.

References


This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.