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A346713
Decimal expansion of sqrt(log 2).
1
8, 3, 2, 5, 5, 4, 6, 1, 1, 1, 5, 7, 6, 9, 7, 7, 5, 6, 3, 5, 3, 1, 6, 4, 6, 4, 4, 8, 9, 5, 2, 0, 1, 0, 4, 7, 6, 3, 0, 5, 8, 8, 8, 5, 2, 2, 6, 4, 4, 4, 0, 7, 2, 9, 1, 6, 6, 8, 2, 9, 1, 1, 7, 2, 3, 4, 0, 7, 9, 4, 3, 5, 1, 9, 7, 3, 0, 4, 6, 3, 7, 1, 4, 8, 9, 9, 8, 0
OFFSET
0,1
COMMENTS
Represents a transcendental number.
REFERENCES
Ludwig Seidel, Ueber eine Darstellung des Kreisbogens, des Logarithmus und des elliptischen Integrales erster Art durch unendliche Producte, Borchardt J., (1871), vol. 73, pp. 273-291.
FORMULA
Equals Product_{k>=1} (2/(2^(1/2^k) + 1))^(1/2).
Equals sqrt(2*arccoth(3)) = sqrt(A002162).
EXAMPLE
0.8325546111576977563531646448952010476305888522644407291668291172340794351973...
MAPLE
Digits := 120; sqrt(log(2)): evalf(%)*10^91:
ListTools:-Reverse(convert(floor(%), base, 10));
MATHEMATICA
RealDigits[Sqrt[Log[2]], 10, 100][[1]] (* Amiram Eldar, Sep 01 2021 *)
PROG
(Julia)
using Nemo
R = RealField(305); _1 = R(1); _2 = R(2); H = R(1/2)
p = prod((_2/(_2^(_1/_2^k) + 1))^H for k in 1:300)
println(p)
CROSSREFS
Cf. A002162.
Sequence in context: A346718 A119277 A273556 * A154014 A063568 A302138
KEYWORD
nonn,cons
AUTHOR
Peter Luschny, Sep 01 2021
STATUS
approved