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 A119256 Successively better denominators for estimating base 10 logs of 2, 3, 4, 5, 6, 7, 8 and 9. "Better" is defined by the RMS error of the best numerators for each given denominator. 1

%I #3 Mar 30 2012 18:34:45

%S 1,4,7,10,13,23,40,63,176,239,329,568,10381,49128,60974,281746,342720,

%T 7484108,11452573,18936681,44390284,55842857

%N Successively better denominators for estimating base 10 logs of 2, 3, 4, 5, 6, 7, 8 and 9. "Better" is defined by the RMS error of the best numerators for each given denominator.

%H <a href="http://mcraefamily.com/MathHelp/MentalMathLog.htm">Estimating Log Base 10</a>

%H Karl's Calculus Tutor: <a href="http://www.karlscalculus.org/l6_3-2.html">Log base 10 tricks (to the 40th degree)</a>

%e a(6)=40 because the square root of the mean of (12-40*log(2))^2, (19-40*log(3))^2, (24-40*log(4))^2, (28-40*log(5))^2, (31-40*log(6))^2, (34-40*log(7))^2, (36-40*log(8))^2 and (38-40*log(9))^2 is smaller than the RMS values obtained using any denominator smaller than 40.

%K base,nonn

%O 0,2

%A _Graeme McRae_, May 10 2006

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