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-0.6650700487648522920... (another Prime Pages' Curiosity) |
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-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.
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