Economical Number

A number n is called an economical number if the number of digits in the prime factorization of n (including powers) uses fewer digits than the number of digits in n. 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.

See also

Equidigital Number, Evil Number, Happy Number, Lucky Number, Odious Number, Unhappy Number, Wasteful Number

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Hess, R. I. "Solution to Problem 2204(b)." J. Recr. Math. 28, 67, 1996-1997.Pinch, R. G. E. "Economical Numbers.", C. "Problems & Puzzles: Puzzle 053-Sequences of Consecutive Economical Numbers.", 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."

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Economical Number

Cite this as:

Weisstein, Eric W. "Economical Number." From MathWorld--A Wolfram Web Resource.

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