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Revision History for A196737

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Decimal expansion of (4*Pi^2)/sqrt(35) = A212002/A010490.
(history; published version)
#40 by Harvey P. Dale at Tue Jan 26 13:55:17 EST 2021
STATUS

editing

approved

#39 by Harvey P. Dale at Tue Jan 26 13:55:15 EST 2021
MATHEMATICA

RealDigits[(4Pi^2)/Sqrt[35], 10, 120][[1]] (* Harvey P. Dale, Jan 26 2021 *)

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approved

editing

#38 by Michel Marcus at Wed Aug 12 11:29:03 EDT 2020
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reviewed

approved

#37 by Joerg Arndt at Wed Aug 12 11:19:51 EDT 2020
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proposed

reviewed

#36 by Andrey Zabolotskiy at Wed Aug 12 08:02:00 EDT 2020
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editing

proposed

Discussion
Wed Aug 12
11:19
Joerg Arndt: Oh yes. Thanks.
#35 by Andrey Zabolotskiy at Wed Aug 12 08:01:15 EDT 2020
COMMENTS

Observation: Where G is the universal gravitational constant = A070058 (= 6.67384(80)*10^-11 m^3*kg^-1*s^-2), GM is the standard gravitational parameter, and M'_pbh is one estimate of the mass of a primordial black hole with evaporation time equal to the age of the universe (~ 10^11 kg; see link by Andrew Hamilton below), then this sequence approximates G*M'_pbh*(4*Pi^2)/GM = G*M'_pbh*seconds^2/meter^3. Were this formula to be exact, then, based on the CODATA 2010 value for G, the mass of such a primordial black hole, rounded to 6 decimal places, would be equal to 0.999885*10^11 kg, a figure subject to change based on future empirical measurements of G. Coincidentally, 99.9885(70)% is the estimated relative abundance of the hydrogen-1 isotope (aka "protium") here on planet Earth.

Alternatively, from the formula for a pendulum, T = 2*Pi*sqrt(L/g), where L = Length, T = period and g is acceleration due to gravity, it follows that this sequence is exactly equal to (g*T^2*(h-bar/2))/(L*Spin(5/2)); h-bar/2 = h/(4*Pi) = A003676/(10*A019694) ~ A003676*A081821*A003671*A005600. - Raphie Frank, Jan 04 2013

LINKS

B. J. Carr, <a href="http://arxiv.org/abs/astro-ph/0511743">Primordial black holes: do they exist and are they useful?</a>, Queen Mary University of London.

Andrew Hamilton, <a href="https://jila.colorado.edu/~ajsh/bh/hawk.html">Hawking Radiation</a>, University of Colorado at Boulder.

Wikipedia, <a href="http://en.wikipedia.org/wiki/Gravitational_constant">Gravitational constant</a>

Wikipedia, <a href="http://en.wikipedia.org/wiki/Isotopes_of_hydrogen">Isotopes of hydrogen</a>

Wikipedia, <a href="http://en.wikipedia.org/wiki/Pendulum">Pendulum</a>

Wikipedia, <a href="http://en.wikipedia.org/wiki/Planck_constant">Planck constant</a>

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approved

editing

Discussion
Wed Aug 12
08:02
Andrey Zabolotskiy: Numerology.
#34 by Susanna Cuyler at Sat Nov 09 08:19:13 EST 2019
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reviewed

approved

#33 by Joerg Arndt at Sat Nov 09 01:17:51 EST 2019
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proposed

reviewed

#32 by Michel Marcus at Sat Nov 09 00:50:40 EST 2019
STATUS

editing

proposed

#31 by Michel Marcus at Sat Nov 09 00:49:51 EST 2019
LINKS

Andrew Hamilton, <a href="httphttps://casajila.colorado.edu/~ajsh/bh/hawk.html">Hawking Radiation</a> , University of Colorado at Boulder.

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approved

editing

Discussion
Sat Nov 09
00:50
Michel Marcus: link has been moved