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Integer pair values {n,m} near the line: m=-Log[2]/Log[3] + (Log[4]/Log[3])*n Based on musical scales of the Pythagorean triangle type{3,4,5} where 4^n/3^m is near 2. The line gives values of 2 exactly for real numbers.
1

%I #4 Mar 30 2012 17:34:21

%S 10,12,33,41,52,65,75,94,94,118,117,147,136,171,159,200,178,224,201,

%T 253

%N Integer pair values {n,m} near the line: m=-Log[2]/Log[3] + (Log[4]/Log[3])*n Based on musical scales of the Pythagorean triangle type{3,4,5} where 4^n/3^m is near 2. The line gives values of 2 exactly for real numbers.

%C Identity: 4^x/3^(-Log[2]/Log[3] + (Log[4]/Log[3]) x)==2 More inclusive Identity: ( any a0,b0,x) a0^x/b0^(-Log[2]/Log[b0] + (Log[a0]/Log[b0]) x)==2

%F {n,m}: If m=-Log[2]/Log[3] + (Log[4]/Log[3])*n is 1% from the Integer m

%e {10, 12}, ->N[4^10/3^12]=1.97308

%e {33, 41}, ->2.02306

%e {52, 65}, ->1.96896

%e {75, 94}, ->2.01884

%e {94, 118} ->1.96486

%t g[x_] = -Log[2]/Log[3] + (Log[4]/Log[3]) x; Delete[Union[Table[Flatten[Table[If[(g[n] - 0.02) <= m && (g[n] + 0.02 >= m), {n, m}, {}], {n, 1, m}], 1], {m, 1, 300}]], 1]; Flatten[%]

%Y Cf. A133403.

%K nonn,uned

%O 1,1

%A _Roger L. Bagula_, Nov 24 2007

%E This appears to be a mixture of two sequences? - _N. J. A. Sloane_, Nov 25 2005