A143301 Decimal expansion of the Hall-Montgomery constant.

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, 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, 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

Offset

0,2

Comments

Named after Richard Roxby Hall and Hugh Lowell Montgomery. - Amiram Eldar, Aug 25 2020

References

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

Links

Table of n, a(n) for n=0..104.

Andrew Granville and Kannan Soundararajan, The spectrum of multiplicative functions, Annals of Mathematics, Vol. 153, No. 2 (2001), pp. 407-470.

R. R. Hall, Proof of a conjecture of Heath-Brown concerning quadratic residues, Proceedings of the Edinburgh Mathematical Society, Vol. 39, No. 3 (1996), pp. 581-588.

Eric Weisstein's World of Mathematics, Hall-Montgomery Constant.

Formula

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

Equals (1 - A126689)/2. - Amiram Eldar, Aug 25 2020

Example

0.17150049314153606586...

Mathematica

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

Prog

(Python)
from mpmath import mp, pi, e, polylog, sqrt
mp.dps=106
print([int(z) for z in list(str(1 + pi**2/6 + 2* polylog(2, - sqrt(e)))[2:-1])]) # Indranil Ghosh, Jul 04 2017

Crossrefs

Cf. A126689.

Sequence in context: A085467 A186168 A117182 * A225459 A317847 A181722

Adjacent sequences: A143298 A143299 A143300 * A143302 A143303 A143304

Keyword

nonn,cons

Author

Eric W. Weisstein, Aug 05 2008

Status

approved