[asqjqlay] The Twilight constant

As popularized in the movie Twilight. (Is it in the book as well?)

The square root of pi = √π ≈ 1.772453850905516027298167483341145182797549456122387128213807789852 91128459103218137495065673854466541622682362428257066623615286572442 ... ≈ [1; 1, 3, 2, 1, 1, 6, 1, 28, 13, 1, 1, 2, 18, 1, 1, 1, 83, 1, 4, 1, 2, 4, 1, 288, 1, 90, 1, 12, 1, 1, 7, 1, 3, 1, 6, 1, 2, 71, 9, 3, 1, 5, 36, 1, 2, 2, 1, 1, 1, 2, 5, 9, 8, 1, 7, 1, 2, 2, 1, 63, 1, 4, 3, 1, 6, 1, 1, 1, 5, 1, 9, 2, 5, 4, 1, 2, 1, 1, 2, 20, 1, 1, 2, 1, 10, 5, 2, 1, 100, 11, 1, 9, 1, 2, 1, 1, 1, 1, 3, 2, 2, 3, 1, 2, 7, 1, 7, 2, 2, 2, 11, 1, 1, 2, 9, 1, 9, 2, 1, 1, 3, 1, 1, 1, 2, 1, 3, 3, 1, 7, 2, 1, 4, 12, 5, 3, 2, 1, 1, 2, 2, 3, 5, 2, 49, 1, 1, 3, 1, 3, 1, 23, 1, 5, 1, 2, 1, 4, 1, 8, 1, 1, 2, 1, 1, 49, 1, 16, 2, 1, 3, 1, 4, 25, 1, 1, 1, 13, 1, 19, 23, 1, 13, 1, 2, 1, 1, 4, 4, 1, 1, 1, 20, 2, 4, 2, 6, 5, 4, 3, 7, 1, 2, 25, 16, 3, 1, 1, 5, 2, 4, 3, 2, 1, 5, 2, 1, 9, 1, 28, 1, 1, 1, 1, 18, 1, 113, 4, 1, 72, 4, 1, 24, 5, 2, 3, 1, 33, 6, 12, 28, 1, 1, 3, 5, 4, 2, 2, 2, 3, 2, 1, 1, 1, 2, 2, 1, 3, 5, 1, 5, 1, 1, 2, 5, 1, 1, 1, 1, 1] (continued fraction)

But thanks to the Inverse Symbolic Calculator, we can also derive that 1.77245 ≈ K-C^ζ(5), where K = Khinchin's constant ≈ 2.6854520011, C = Catalan's constant ≈ 0.9159655942, and ζ(5) = Riemann's Zeta Function (evaluated at 5) = 1 + 2^-5 + 3^-5 + 4^-5 + 5^-5 + 6^-5 ... ≈ 1.0369277551.

"I don't want to know what Khinchin's constant minus Catalan's constant to the power of zeta five is." (Isabella Swan)