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A343615
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Decimal expansion of P_{3,2}(5) = Sum 1/p^5 over primes == 2 (mod 3).
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2
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0, 3, 1, 5, 7, 7, 1, 3, 5, 7, 1, 9, 0, 0, 3, 9, 4, 1, 9, 5, 6, 0, 3, 3, 7, 8, 0, 3, 4, 3, 7, 1, 6, 3, 9, 6, 3, 4, 7, 7, 7, 2, 9, 9, 6, 3, 8, 3, 2, 4, 8, 6, 1, 4, 5, 7, 9, 0, 2, 5, 8, 3, 4, 1, 2, 2, 8, 2, 9, 7, 5, 5, 7, 1, 9, 8, 1, 1, 7, 3, 0, 3, 9, 1, 5, 9, 6, 1, 1, 0, 7, 5, 2, 9, 7, 6, 2, 6, 2
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OFFSET
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0,2
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COMMENTS
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The prime zeta modulo function P_{m,r}(s) = Sum_{primes p == r (mod m)} 1/p^s generalizes the prime zeta function P(s) = Sum_{primes p} 1/p^s.
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LINKS
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FORMULA
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P_{3,2}(5) = P(5) - 1/3^5 - P_{3,1}(5).
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EXAMPLE
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0.0315771357190039419560337803437163963477729963832486145790258341228297557...
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PROG
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(PARI) s=0; forprimestep(p=2, 1e8, 3, s+=1./p^4); s \\ For illustration: using primes up to 10^N gives about 3N+2 (= 26 for N=8) correct digits.
(PARI) A343615_upto(N=100, s=5)={localprec(N+5); digits((sumeulerrat(1/p^s)-1/3^s-PrimeZeta31(s)+1)\.1^N)[^1]} \\ see A175644 for the function PrimeZeta31, A343612 for a function PrimeZeta32
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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