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A328498
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Decimal expansion of Sum_{(p, q) runs through the twin primes} ((p mod 4) - 2) * (1/p + 1/q).
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0
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OFFSET
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0,2
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COMMENTS
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Because Viggo Brun's constant is 1.90216058... it is easy to find these 2 new constants:
(1/3 + 1/5) + (1/11 + 1/13) + (1/59 + 1/61) + (1/71 + 1/73) + ... = 1.04283048...
(1/5 + 1/7) + (1/17 + 1/19) + (1/29 + 1/31) + (1/41 + 1/43) + ... = 0.85933010...
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LINKS
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EXAMPLE
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(1/3 + 1/5) - (1/5 + 1/7) + (1/11 + 1/13) - (1/17 + 1/19) - (1/29 + 1/31) + ... = 0.183500386... +- 0.000000002
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PROG
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(PARI) my(p = 3, s = 0.0); forprime(n = 5, 10^16, if(n-p == 2, if(p%4 == 3, s+= 1/p + 1/n, s+= -1/p - 1/n)); p = n); 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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