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A306539
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Decimal expansion of Sum (1/p - 1/q) as (p, q) runs through the twin primes.
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3
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2, 1, 5, 9, 6, 7, 9, 4, 9, 9, 0, 2, 3, 7, 4
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OFFSET
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0,1
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COMMENTS
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If a = Sum (1/p) as (p, q) runs through the twin primes and
If b = Sum (1/q) as (p, q) runs through the twin primes, then
a + b = 1.902160583209... (Brun's constant) and
a - b = 0.215967949902374... (This constant).
So a = Sum_{n>=1} 1/A001359(n) = 1.059064266555685...
and b = Sum_{n>=1} 1/A006512(n) = 0.843096316653315... are 2 new constants for twin primes.
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LINKS
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FORMULA
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EXAMPLE
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0.215967949902374...
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PROG
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(PARI) p=2; s=0.0; forprime(n=3, 1e14, if(n-p==2, s+=(1/p-1/n)); p=n; ); print1(s)
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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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