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A242187 Decimal expansion of Sum_{n>=1} 1/(prime(n)*prime(n+1)*prime(n+2)): Sum of reciprocals of products of three successive primes. 1
4, 7, 4, 9, 4, 4, 3, 6, 0, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
-1,1
COMMENTS
Since p(n+1) > p(n) and p(n+2) > p(n), p(n)*p(n+1)*p(n+2) > p(n)^3 and 1/[p(n)*p(n+1)*p(n+2)] < 1/p(n)^3. Because Sum_{n>=1} 1/p(n)^3 = A085541 converges, Sum_{n>=1} 1/(p(n)*p(n+1)*p(n+2)) converges, too.
Greater than 0.04749443601963321719578... - R. J. Mathar, May 11 2014
LINKS
EXAMPLE
0.04749443601... = Sum_{n>=1} 1/A046301(n) = 1/(2*3*5) + 1/(3*5*7) + 1/(5*7*11) + 0.020286072... (primes 10 < p(n+1) < 100) + ...
MAPLE
proc(q) local n;
print(evalf(add(1/(ithprime(n)*ithprime(n+1)*ithprime(n+2)), n=1..q), 200));
end:
CROSSREFS
Sequence in context: A094765 A170863 A021682 * A094692 A059139 A329740
KEYWORD
nonn,cons,more
AUTHOR
Timothy Varghese, May 06 2014
EXTENSIONS
Offset corrected by Jon E. Schoenfield, Mar 21 2021
STATUS
approved

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Last modified March 5 02:31 EST 2024. Contains 370537 sequences. (Running on oeis4.)