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A054965 Beatty sequence for log_3(10), i.e., for 1/log_10(3); so largest exponent of 3 which produces an n-digit decimal number.

%I A054965 #24 Feb 16 2025 08:32:42
%S A054965 2,4,6,8,10,12,14,16,18,20,23,25,27,29,31,33,35,37,39,41,44,46,48,50,
%T A054965 52,54,56,58,60,62,64,67,69,71,73,75,77,79,81,83,85,88,90,92,94,96,98,
%U A054965 100,102,104,106,108,111,113,115,117,119,121,123,125,127,129,132,134,136
%N A054965 Beatty sequence for log_3(10), i.e., for 1/log_10(3); so largest exponent of 3 which produces an n-digit decimal number.
%H A054965 Paolo Xausa, <a href="/A054965/b054965.txt">Table of n, a(n) for n = 1..10000</a>
%H A054965 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence</a>.
%H A054965 <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>.
%F A054965 a(n) = floor(n/log_10(3)) = log_3(A074118(n)) = A062153(A074118(n)).
%e A054965 log_10(3) = 0.477121... so a(11) = floor(11/0.477121...) = floor(23.0549...) = 23; 3^23 = 94143178827 is the largest 11 decimal digit power of 3.
%t A054965 Floor[Range[100]*Log[3, 10]] (* _Paolo Xausa_, Jul 11 2024 *)
%o A054965 (PARI) a(n) = n*log(10)\log(3); \\ _Michel Marcus_, Aug 03 2017
%Y A054965 Cf. A062153, A066343, A074118, A152566.
%K A054965 base,nonn
%O A054965 1,1
%A A054965 _Henry Bottomley_, Dec 13 2002