An economical number is an integer whose prime factorization,
including its written exponents, contains fewer decimal
digits than
itself. Exponents equal to 1 are omitted. The first
few economical numbers are 125, 128, 243, 256, 343, 512, 625, 729, ... (OEIS A046759).
Pinch (1998, p. 4) shows that, under a hypothesis related to the twin prime conjecture, there are arbitrarily long sequences of consecutive economical
numbers. His terminology includes equidigital numbers
among economical numbers. In this broader sense, he exhibits nine consecutive integers starting at 1034429177995381247. This example is
not a run of nine economical numbers under the strict convention used here.
Hess, R. I. "Solution to Problem 2204(b)." J. Recr. Math.28, 67, 1996-1997.Pinch, R. G. E.
"Economical Numbers." 9 Feb 1998. https://arxiv.org/abs/math/9802046.Rivera,
C. "Problems & Puzzles: Puzzle 053-Sequences of Consecutive Economical Numbers."
https://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."
whose prime factorization,
including its written exponents, contains fewer decimal
digits than 
itself. Exponents equal to 1 are omitted. The first
few economical numbers are 125, 128, 243, 256, 343, 512, 625, 729, ... (OEIS A046759).
