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Search: id:A133403
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| A133403 |
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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. |
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+0
2
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| 12, 18, 41, 64, 53, 83, 94, 148, 106, 167, 147, 232, 159, 251
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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FORMULA
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{n,m}: If m=-Log[2]/Log[2] + (Log[3]/Log[2])*n is 1% from the Integer m
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EXAMPLE
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{12, 18, 2.02729},
{41, 64, 1.97721},
{53, 83, 2.00418},
{94, 148, 1.98134},
{106, 167, 2.00837},
{147, 232, 1.98548},
{159, 251, 2.01257}
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MATHEMATICA
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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[%]
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CROSSREFS
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Cf. A132313.
Sequence in context: A007371 A079479 A124205 this_sequence A119147 A086301 A018957
Adjacent sequences: A133400 A133401 A133402 this_sequence A133404 A133405 A133406
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 24 2007
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EXTENSIONS
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This appears to be a mixture of two sequences? - njas, Nov 25 2005
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