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
Examples
0.17150049314153606586...
References
- Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, pp. 205-207.
Links
- Thomas Bloom, Problem 121, Erdős Problems.
- 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).
- Terence Tao, Erdős problem database, see no. 121.
- Eric Weisstein's World of Mathematics, Hall-Montgomery Constant.
Programs
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Mathematica
RealDigits[1+Pi^2/6+2PolyLog[2,-Sqrt[E]],10,120][[1]] (* Harvey P. Dale, Jul 18 2013 *)
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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
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
Comments