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A331369 Decimal expansion of Sum_{(p1, p2) is twin prime pair} 1/p1 + 1/p2 - log(p2/p1). 1
0, 2, 9, 9, 8, 1, 7, 1, 0, 8, 3, 8, 9, 0, 6, 2, 6, 9, 6, 8, 2, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
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.
LINKS
FORMULA
Equals Sum_{k >= 1} 1/A001359(k) + 1/A006512(k) - log(A006512(k)/A001359(k)).
EXAMPLE
0.0299817108389062696826...
PROG
(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)
CROSSREFS
Sequence in context: A266274 A003678 A201683 * A197394 A198942 A168333
KEYWORD
nonn,cons,more
AUTHOR
Dimitris Valianatos, May 03 2020
STATUS
approved

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)