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A143301 Decimal expansion of the Hall-Montgomery constant. 5

%I #21 Aug 25 2020 04:21:56

%S 1,7,1,5,0,0,4,9,3,1,4,1,5,3,6,0,6,5,8,6,0,4,3,9,9,7,1,5,5,5,2,1,2,1,

%T 0,9,6,2,2,2,6,2,9,0,4,2,2,9,5,5,0,8,4,1,7,1,4,2,1,1,0,9,1,8,2,3,6,9,

%U 8,6,0,5,5,9,4,3,0,8,5,7,7,9,8,7,9,7,1,1,9,8,0,8,6,8,0,0,8,1,7,3,0,6,4,2,3

%N Decimal expansion of the Hall-Montgomery constant.

%C Named after Richard Roxby Hall and Hugh Lowell Montgomery. - _Amiram Eldar_, Aug 25 2020

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, pp. 205-207.

%H Andrew Granville and Kannan Soundararajan, <a href="https://www.jstor.org/stable/2661346">The spectrum of multiplicative functions</a>, Annals of Mathematics, Vol. 153, No. 2 (2001), pp. 407-470.

%H R. R. Hall, <a href="https://doi.org/10.1017/S0013091500023324">Proof of a conjecture of Heath-Brown concerning quadratic residues</a>, Proceedings of the Edinburgh Mathematical Society, Vol. 39, No. 3 (1996), pp. 581-588.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Hall-MontgomeryConstant.html">Hall-Montgomery Constant</a>.

%F Equals 1 + Pi^2/6 + 2*PolyLog(2, -sqrt(e)).

%F Equals (1 - A126689)/2. - _Amiram Eldar_, Aug 25 2020

%e 0.17150049314153606586...

%t RealDigits[1+Pi^2/6+2PolyLog[2,-Sqrt[E]],10,120][[1]] (* _Harvey P. Dale_, Jul 18 2013 *)

%o (Python)

%o from mpmath import mp, pi, e, polylog, sqrt

%o mp.dps=106

%o print([int(z) for z in list(str(1 + pi**2/6 + 2* polylog(2, - sqrt(e)))[2:-1])]) # _Indranil Ghosh_, Jul 04 2017

%Y Cf. A126689.

%K nonn,cons

%O 0,2

%A _Eric W. Weisstein_, Aug 05 2008

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Last modified March 29 10:22 EDT 2024. Contains 371268 sequences. (Running on oeis4.)