cp's OEIS Frontend

A377478 a(n) = first frugal number > 1 in base n.

%I A377478 #11 Jan 01 2025 14:43:27
%S A377478 27,32,27,27,81,64,64,81,125,125,243,243,243,243,256,343,343,512,512,
%T A377478 512,512,625,625,625,729,729,1024,1024,1024,1024,1024,1331,1331,1331,
%U A377478 1331,2048,2048,2048,2048,2048,2048,2048,2048,2048,2187,2401,2401,2401,3125,3125
%N A377478 a(n) = first frugal number > 1 in base n.
%C A377478 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).
%C A377478 Following the definition by Pinch (1998), 1 is considered a frugal number.
%H A377478 Richard G. E. Pinch, <a href="https://doi.org/10.48550/arXiv.math/9802046">Economical numbers</a>, arXiv:math/9802046 [math.NT], 1998.
%H A377478 Giovanni Resta, <a href="https://www.numbersaplenty.com/set/frugal_number/">Frugal numbers</a>, Numbers Aplenty, 2013.
%H A377478 Wikipedia, <a href="https://en.wikipedia.org/wiki/Frugal_number">Frugal number</a>.
%e A377478 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.
%e A377478 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.
%t A377478 Module[{m}, Table[m = 1; While[Total[IntegerLength[Select[Flatten[FactorInteger[++m]], # > 1 &], n]] >= IntegerLength[m, n]]; m, {n, 2, 50}]]
%Y A377478 Column k = 2 of A379538.
%Y A377478 Cf. A046759, A379537.
%K A377478 nonn,base
%O A377478 2,1
%A A377478 _Paolo Xausa_, Dec 28 2024