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A343614
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Decimal expansion of P_{3,2}(4) = Sum 1/p^4 over primes == 2 (mod 3).
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2
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0, 6, 4, 1, 8, 6, 1, 4, 5, 6, 9, 6, 5, 5, 7, 7, 7, 8, 9, 9, 0, 0, 9, 9, 0, 8, 6, 5, 8, 7, 4, 0, 2, 7, 3, 6, 8, 0, 9, 7, 5, 6, 3, 6, 2, 3, 4, 8, 6, 8, 0, 6, 4, 0, 8, 8, 4, 6, 2, 5, 4, 9, 2, 2, 5, 0, 6, 2, 1, 9, 1, 2, 6, 2, 1, 9, 3, 8, 9, 9, 8, 6, 4, 7, 9, 6, 5, 5, 2, 6, 9, 1, 6, 3, 8, 2, 2, 4, 0, 7
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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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P_{3,2}(4) = 0.06418614569655777899009908658740273681...
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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) A343614_upto(N=100)={localprec(N+5); digits((PrimeZeta32(4)+1)\.1^N)[^1]} \\ see 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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