cp's OEIS Frontend

A377010 Decimal expansion of the asymptotic mean of A376928: lim_{m->oo} (1/m) * Sum_{k=1..m} A376928(k).

%I A377010 #6 Oct 13 2024 11:17:30
%S A377010 1,7,4,4,6,6,3,4,0,5,0,1,7,4,0,1,9,2,3,4,5,7,3,0,8,8,8,3,5,2,5,8,1,7,
%T A377010 0,3,5,9,8,5,7,0,0,5,0,4,3,6,4,0,9,0,6,1,6,6,7,2,2,3,3,0,0,7,9,4,1,1,
%U A377010 3,3,3,1,0,2,8,5,9,8,4,6,5,6,2,1,1,8,7,2,6,0,8,6,6,3,1,7,1,2,7,6,2,9,9,0,2
%N A377010 Decimal expansion of the asymptotic mean of A376928: lim_{m->oo} (1/m) * Sum_{k=1..m} A376928(k).
%F A377010 Equals 1/2 + Sum_{p prime} p * (1/p# - 1/nextprime(p)#), where nextprime(p) = A151800(p) and p# = A034386(p).
%F A377010 Equals 1/2 + Sum_{k>=1} prime(k) * (1/A002110(k) - 1/A002110(k+1)).
%e A377010 1.74466340501740192345730888352581703598570050436409...
%o A377010 (PARI) \p 120
%o A377010 f(k) = prod(i = 1, k, prime(i));
%o A377010 1/2 + suminf(k = 1, prime(k) * (1/f(k) - 1/f(k+1)))
%Y A377010 Cf. A002110, A034386, A151800, A249270, A376928.
%K A377010 nonn,cons
%O A377010 1,2
%A A377010 _Amiram Eldar_, Oct 12 2024