Frugal number

A frugal number is a natural number that has more digits than the number of digits in its prime factorization (including exponents).[1] For example, using base-10 arithmetic, the first few frugal numbers are 125 (53), 128 (27), 243 (35), and 256 (28). Frugal numbers also exist in other bases; for instance, in binary arithmetic thirty-two is a frugal number, since 10101 = 100000.

The base-10 frugal numbers up to 2000 are:

125, 128, 243, 256, 343, 512, 625, 729, 1024, 1029, 1215, 1250, 1280, 1331, 1369, 1458, 1536, 1681, 1701, 1715, 1792, 1849, 1875 (sequence A046759 in the OEIS)

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

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


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