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%I #4 Mar 30 2012 17:34:22
%S 12,18,41,64,53,83,94,148,106,167,147,232,159,251
%N Integer pair values {n,m} near the line: m=-Log[2]/Log[2] + (Log[3]/Log[2])*n Based on musical scales of the Pythagorean triangle type{2,3,Sqrt[13]} where 3^n/2^m is near 2. The line gives values of 2 exactly for real numbers.
%C Identity: 3^x/2^(-Log[2]/Log[2] + (Log[3]/Log[2]) x)==2 More inclusive Identity: ( any a0,b0,x) a0^x/b0^(-Log[2]/Log[b0] + (Log[a0]/Log[b0]) x)==2 This sequence is based on the traditional Pythagorean musical scale.
%F {n,m}: If m=-Log[2]/Log[2] + (Log[3]/Log[2])*n is 1% from the Integer m
%e {12, 18, 2.02729},
%e {41, 64, 1.97721},
%e {53, 83, 2.00418},
%e {94, 148, 1.98134},
%e {106, 167, 2.00837},
%e {147, 232, 1.98548},
%e {159, 251, 2.01257}
%t g[x_] = -Log[2]/Log[2] + (Log[3]/Log[2]) 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. A132313.
%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
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