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A143301
Decimal expansion of the Hall-Montgomery constant.
5
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
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.
Terence Tao, On product representations of squares, arXiv:2405.11610 [math.NT], May 2024. See page 2, (1.2).
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
Equals 1 - A246849. - Hugo Pfoertner, May 25 2024
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
Sequence in context: A085467 A186168 A117182 * A225459 A317847 A181722
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Aug 05 2008
STATUS
approved