A143301 - OEIS

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

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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.

Thomas Bloom, Problem 121, Erdős Problems.

Erdős problems database contributors, Erdős problem database, see no. 121.

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)