|
| |
|
|
A161771
|
|
Decimal expansion of exp^2(pi*sqrt163) 70^2
|
|
4
| |
|
|
3, 3, 7, 7, 3, 6, 8, 7, 5, 8, 7, 6, 9, 3, 5, 4, 7, 1, 4, 6, 6, 3, 1, 9, 6, 3, 2, 5, 0, 6, 0, 2, 4, 4, 6, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 2, 3, 1, 9, 3, 5, 6, 6, 2, 5, 2, 4, 9, 5, 7, 7, 1, 0, 4, 4, 1, 2, 4, 0, 6, 5, 9, 7, 4, 0, 9, 9, 7, 1, 0, 0, 6, 8, 5, 9, 8, 5, 1, 9, 3, 7, 0, 6, 5, 2, 2, 3, 2, 2, 8, 1, 6, 9
(list; constant; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 39,1
|
|
|
COMMENTS
| Where exp^(pi*sqrt163) is the Ramanujan constant and 70^2 is related to the norm vector 0 of the Leech lattice where 1^2+2^2+3^2...+22^2+23^2+24^2 = 70^2 A curiosity is: exp^2(pi*sqrt163) 70^2 ~ hc/piGm^2 where all physics values are CODATA 2006 and m = neutron mass and exp^2(pi*sqrt163) 70^2 = 3.377368...x 10^38 and hc/piGm^2 = 3.37700 x 10^38 (+- 0.00050) where 0.00050 = u_c which is the combined standard uncertainty.
This can also be expressed in a nice symmetric form in terms of the square of the neutron mass in units of Planck mass: where hc/2piGm^2 = (Mp/m)^2 (Mp = Planck mass and m = neutron mass) and (exp^2(pi*sqrt163)70^2)/2 ~ (Mp/m)^2 . Note the divisor 2 in this case which yields (exp^2(pi*sqrt163)70^2)/2 = 168868437938467735733159816253012231600.00000040115967 [From Mark A. Thomas (monstrousgaugetheory(AT)gmail.com), Jul 02 2009]
|
|
|
LINKS
| R. Munafo,Notable Properties of Specific Numbers [From Mark A. Thomas (monstrousgaugetheory(AT)gmail.com), Jul 02 2009]
|
|
|
FORMULA
| exp^2(pi*sqrt163) 70^2
|
|
|
EXAMPLE
| exp^2(pi*sqrt163) 70^2 = 337736875876935471466319632506024463200.00000080231935662524957710441240659...
|
|
|
MATHEMATICA
| ((e^((pi)sqrt163))^2 70^2)
|
|
|
CROSSREFS
| Near relation to A160514 and A160515
Sequence in context: A069981 A000199 A201932 * A160515 A105670 A003817
Adjacent sequences: A161768 A161769 A161770 * A161772 A161773 A161774
|
|
|
KEYWORD
| nonn,cons
|
|
|
AUTHOR
| Mark A. Thomas (monstrousgaugetheory(AT)gmail.com), Jun 18 2009
|
| |
|
|
