-0.665070048764852292... is the real root of f(x) = 1 +
(twin_prime(n))x^n = 1 + 3x + 5x^2 + 5x^3 + 7x^4 + 11x^5 +
13x^6 + 17x^7 + 19x^8 + 29x^9 + 31x^10 + 41x^11 + 43x^12 +
59x^13 + 61x^14 + 71x^15 + 73x^16 + ... where for n>0
the coefficient of x^n is the nth twin prime. This power
series with twin prime coefficients is similar to the power
series with prime coefficients, as computed in Finch's
article on Backhouse's constant. Jonathan Vos Post first
described this pseudo-Backhouse constant; T. D. Noe wrote
the Mathematica code and computed it to 100 decimal places.
T. D. Noe speculates that the constant is transcendental.
-0. 6650700487 6485229204 3487143280
8714589422 8105261364 6060424028 5906094123 4037072841 9590091015 6464006499