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A343613
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Decimal expansion of P_{3,2}(3) = Sum 1/p^3 over primes == 2 (mod 3).
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4
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1, 3, 4, 1, 2, 5, 1, 7, 8, 9, 1, 5, 4, 6, 3, 5, 4, 0, 4, 2, 8, 5, 9, 9, 3, 2, 9, 9, 9, 9, 4, 3, 1, 1, 9, 8, 9, 9, 5, 8, 7, 9, 9, 1, 9, 7, 5, 2, 1, 6, 8, 3, 3, 7, 3, 7, 0, 5, 9, 9, 1, 0, 6, 1, 5, 3, 8, 5, 3, 3, 4, 9, 9, 5, 6, 0, 4, 7, 9, 3, 7, 6, 7, 1, 5, 2, 8, 6, 5, 3, 7, 4, 0, 4, 0, 3, 4, 4, 4, 3, 3, 6, 7, 8, 6
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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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EXAMPLE
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0.134125178915463540428599329999431198995879919752168337370599106153853349956...
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PROG
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(PARI) s=0; forprimestep(p=2, 1e8, 3, s+=1./p^3); s \\ For illustration: using primes up to 10^N gives about 2N+2 (= 18 for N=8) correct digits.
(PARI) A343613_upto(N=100)={localprec(N+5); digits((PrimeZeta32(3)+1)\.1^N)[^1]} \\ see A343612 for the 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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