A132313 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.

10, 12, 33, 41, 52, 65, 75, 94, 94, 118, 117, 147, 136, 171, 159, 200, 178, 224, 201, 253

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..20.

Formula

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

Example

{10, 12}, ->N[4^10/3^12]=1.97308
{33, 41}, ->2.02306
{52, 65}, ->1.96896
{75, 94}, ->2.01884
{94, 118} ->1.96486

Mathematica

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[%]

Crossrefs

Cf. A133403.

Sequence in context: A080470 A087217 A044972 * A324745 A367148 A267393

Adjacent sequences: A132310 A132311 A132312 * A132314 A132315 A132316

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