A number 
is called an economical number if the number of digits in the prime factorization
of 
(including powers) uses fewer digits than the number of digits in 
. The first few economical numbers are 125, 128, 243, 256,
343, 512, 625, 729, ... (OEIS A046759). Pinch
shows that, under a plausible hypothesis related to the twin
prime conjecture, there are arbitrarily long sequences of consecutive economical
numbers, and exhibits such a sequence of length nine starting at 1034429177995381247.
Economical Number
See also
Equidigital Number, Evil Number, Happy Number, Lucky Number, Odious Number, Unhappy Number, Wasteful NumberExplore with Wolfram|Alpha
References
Hess, R. I. "Solution to Problem 2204(b)." J. Recr. Math. 28, 67, 1996-1997.Pinch, R. G. E. "Economical Numbers." http://www.chalcedon.demon.co.uk/publish.html#62.Rivera, C. "Problems & Puzzles: Puzzle 053-Sequences of Consecutive Economical Numbers." http://www.primepuzzles.net/puzzles/puzz_053.htm.Santos, B. R. "Problem 2204. Equidigital Representation." J. Recr. Math. 27, 58-59, 1995.Sloane, N. J. A. Sequence A046759 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Economical NumberCite this as:
Weisstein, Eric W. "Economical Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EconomicalNumber.html