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.

4, 7, 4, 9, 4, 4, 3, 6, 0, 1, 9, 6, 3, 3, 5, 1, 8, 3, 7

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

Table of n, a(n) for n=-1..17.

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

Cf. A046301, A085541, A210473.

Sequence in context: A094765 A170863 A021682 * A094692 A059139 A329740

Adjacent sequences: A242184 A242185 A242186 * A242188 A242189 A242190

Keyword

nonn,cons,more

Author

Timothy Varghese, May 06 2014

Extensions

Offset corrected by Jon E. Schoenfield, Mar 21 2021

9 more terms from Jon E. Schoenfield, Apr 10 2024

Status

approved