A133403 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.

12, 18, 41, 64, 53, 83, 94, 148, 106, 167, 147, 232, 159, 251

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..14.

Formula

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

Example

{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}

Mathematica

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[%]

Crossrefs

Cf. A132313.

Sequence in context: A197464 A124205 A338259 * A152615 A258088 A259263

Adjacent sequences: A133400 A133401 A133402 * A133404 A133405 A133406

Keyword

nonn,uned

Author

Roger L. Bagula, Nov 24 2007

Extensions

This appears to be a mixture of two sequences? - N. J. A. Sloane, Nov 25 2005

Status

approved