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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 Table of n, a(n) for n=-1..8. 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 STATUS approved

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