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A377010
Decimal expansion of the asymptotic mean of A376928: lim_{m->oo} (1/m) * Sum_{k=1..m} A376928(k).
1
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, 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, 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
OFFSET
1,2
FORMULA
Equals 1/2 + Sum_{p prime} p * (1/p# - 1/nextprime(p)#), where nextprime(p) = A151800(p) and p# = A034386(p).
Equals 1/2 + Sum_{k>=1} prime(k) * (1/A002110(k) - 1/A002110(k+1)).
EXAMPLE
1.74466340501740192345730888352581703598570050436409...
PROG
(PARI) \p 120
f(k) = prod(i = 1, k, prime(i));
1/2 + suminf(k = 1, prime(k) * (1/f(k) - 1/f(k+1)))
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Oct 12 2024
STATUS
approved