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A161771 Decimal expansion of (70*exp(Pi*sqrt(163)))^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; text; 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 [Mark A. Thomas, Jul 02 2009]

LINKS

Table of n, a(n) for n=39..143.

R. Munafo, Notable Properties of Specific Numbers

FORMULA

exp^2(Pi*sqrt(163))*70^2

EXAMPLE

337736875876935471466319632506024463200.00000080231935662524957710441240659...

MATHEMATICA

Exp[Pi Sqrt[163]]^2 70^2

CROSSREFS

Near relation to A160514 and A160515

Sequence in context: A000199 A243099 A201932 * A160515 A105670 A003817

Adjacent sequences:  A161768 A161769 A161770 * A161772 A161773 A161774

KEYWORD

nonn,cons

AUTHOR

Mark A. Thomas, Jun 18 2009

STATUS

approved

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Last modified April 19 00:50 EDT 2015. Contains 256776 sequences.