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A339470
Decimal expansion of log(phi)^2, where phi is the golden ratio (A002390^2).
0
2, 3, 1, 5, 6, 4, 8, 2, 0, 5, 7, 7, 1, 9, 4, 3, 9, 2, 4, 9, 6, 9, 2, 9, 0, 7, 1, 2, 3, 1, 5, 3, 2, 7, 6, 0, 0, 1, 6, 4, 0, 6, 3, 5, 0, 0, 4, 9, 2, 9, 8, 8, 7, 0, 8, 1, 5, 3, 0, 1, 2, 2, 8, 6, 8, 9, 7, 9, 5, 3, 4, 5, 5, 6, 6, 9, 6, 1, 8, 1, 2, 9, 8, 5, 0, 5, 4
OFFSET
0,1
LINKS
FORMULA
Equals arcsinh(1/2)^2 = A002390^2.
Equals (1/2)*Sum_{k>=1} ((k!)^2*(-1)^(k+1))/((2*k)!*k^2) = A086467/2.
Equals (1/3)*(zeta(2) - Sum_{k>=1} ((k!)^2*(-1)^k)/((2*k)!*(2*k+1)^2)).
Equals (1/2)*Sum_{k>=1} (-1)^(k+1)/A002736(k).
EXAMPLE
0.2315648205771943924969290712315327600164063500492988708153012286...
MATHEMATICA
RealDigits[Log[GoldenRatio]^2, 10, 100][[1]] (* Amiram Eldar, Dec 06 2020 *)
PROG
(PARI) asinh(1/2)^2 \\ Michel Marcus, Dec 06 2020
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Robert Bilinski, Dec 06 2020
STATUS
approved