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URL: https://oeis.org/A377478

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A377478
a(n) = first frugal number > 1 in base n.
1
27, 32, 27, 27, 81, 64, 64, 81, 125, 125, 243, 243, 243, 243, 256, 343, 343, 512, 512, 512, 512, 625, 625, 625, 729, 729, 1024, 1024, 1024, 1024, 1024, 1331, 1331, 1331, 1331, 2048, 2048, 2048, 2048, 2048, 2048, 2048, 2048, 2048, 2187, 2401, 2401, 2401, 3125, 3125
OFFSET
2,1
COMMENTS
A frugal number in base n is a number with more digits (in its base n representation) than the total number of digits (in base n representation) of its prime factorization (including exponents > 1).
Following the definition by Pinch (1998), 1 is considered a frugal number.
LINKS
Richard G. E. Pinch, Economical numbers, arXiv:math/9802046 [math.NT], 1998.
Giovanni Resta, Frugal numbers, Numbers Aplenty, 2013.
Wikipedia, Frugal number.
EXAMPLE
a(2) = 27 because 27 = 3^3 = 11_2^11_2; the total number of bits of (11_2, 11_2) = 4 < the number of bits of 27 = 11011_2 (5); and 27 is the first number > 1 with this property.
a(3) = 32 because 32 = 2^5 = 2_3^12_3; the total number of digits of (2_3, 12_3) = 3 < the number of digits in base 3 of 32 = 1012_3 (4); and 32 is the first number > 1 with this property.
MATHEMATICA
Module[{m}, Table[m = 1; While[Total[IntegerLength[Select[Flatten[FactorInteger[++m]], # > 1 &], n]] >= IntegerLength[m, n]]; m, {n, 2, 50}]]
CROSSREFS
Column k = 2 of A379538.
Sequence in context: A228060 A031408 A324248 * A275188 A379537 A198147
KEYWORD
nonn,base
AUTHOR
Paolo Xausa, Dec 28 2024
STATUS
approved