

A161771


Decimal expansion of (70*exp(Pi*sqrt(163)))^2.


5



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
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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 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

G. C. Greubel, Table of n, a(n) for n = 39..10038
R. Munafo, Notable Properties of Specific Numbers
M. A. Thomas, Math Ontological Basis of Quasi FineTuning in Ghc Cosmologies, HAL preprint Id: hal01232022, 2015.
M. A. Thomas, Number Theoretic Structural Approach to Dimensionless Physics Forms, HAL preprint Id: hal01580821 [math.NT], 2017.


FORMULA

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


EXAMPLE

337736875876935471466319632506024463200.00000080231935662524957710...


MAPLE

evalf((70*exp(Pi*sqrt(163)))^2, 120); # Muniru A Asiru, Oct 25 2018


MATHEMATICA

First@ RealDigits[Exp[Pi Sqrt[163]]^2 70^2, 10, 105] (* Mark A. Thomas, Jun 18 2009, edited by Michael De Vlieger, Feb 19 2018 *)


PROG

(PARI) default(realprecision, 100); exp(2*Pi*sqrt(163))*70^2 \\ G. C. Greubel, Oct 24 2018
(MAGMA) SetDefaultRealField(RealField(100)); R:= RealField(); Exp(2*Pi(R)*Sqrt(163))*70^2; // G. C. Greubel, Oct 24 2018


CROSSREFS

Near relation to A160514 and A160515.
Sequence in context: A243099 A324877 A201932 * A160515 A105670 A283996
Adjacent sequences: A161768 A161769 A161770 * A161772 A161773 A161774


KEYWORD

nonn,cons


AUTHOR

Mark A. Thomas, Jun 18 2009


STATUS

approved



