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A282468
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Decimal expansion of the zeta function at 2 of every second prime number.
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1
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1, 4, 4, 7, 1, 5, 5, 8, 6, 6, 8, 8, 7
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OFFSET
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0,2
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COMMENTS
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Note that since p_n > n*log(n), we can place a bound on the tail of the sum:
Sum_{n >= N} (prime(2n))^(-2) <= Sum_{n >= N} (2*n*log(2n))^(-2) <= Integral_{x=N..oo} (2*x*log(2x))^(-2) dx.
Taking the sum over all primes < 10^12, we see that the constant lies between 0.14471558668870 and 0.14471558668873. (End)
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LINKS
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FORMULA
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Equals Sum_{n>=1} 1/A031215(n)^2 = Sum_{n>=1} 1/prime(2n)^2.
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EXAMPLE
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1/3^2 + 1/7^2 + 1/13^2 + 1/19^2 + 1/29^2 + ... = 0.14471558...
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PROG
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(PARI) sum(n=1, 2500000, 1./prime(2*n)^2)
(PARI) \\ see Raza link
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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