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A331369
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Decimal expansion of Sum_{(p1, p2) is twin prime pair} 1/p1 + 1/p2 - log(p2/p1).
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1
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0, 2, 9, 9, 8, 1, 7, 1, 0, 8, 3, 8, 9, 0, 6, 2, 6, 9, 6, 8, 2, 6
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OFFSET
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0,2
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COMMENTS
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Let (p_k, p_(k+1)) twin prime pair. Then log(p_(k+1)/p_k) < 1/p_k + 1/p_(k+1).
Lim_{k -> oo} 1/p_k + 1/p_(k+1) - log(p_(k+1)/p_k) = 0.
This constant is analogous to Euler-Mascheroni constant for twin primes.
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LINKS
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FORMULA
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EXAMPLE
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0.0299817108389062696826...
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PROG
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(PARI) p = 3; st = 0.0; forprime(n = 5, 1e11, if(n - p == 2, st += 1/p + 1/n - log(n/p)); p = n); print(st)
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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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