A381113 - OEIS

%I #4 Feb 17 2025 03:29:52

%S 5,1,5,9,1,4,2,8,5,9,6,5,1,6,4,2,0,3,0,1,3,6,5,8,0,9,7,4,5,0,1,2,5,8,

%T 1,7,2,0,0,0,7,3,0,7,2,1,4,1,9,1,6,7,9,9,3,5,0,0,6,6,3,8,8,6,6,2,4,5,

%U 4,2,4,3,7,8,8,1,0,7,1,2,1,2,1,9,9,5,3,5,3,3,9,3,6,1,5,1,0,5,0,0,1,1,9,4,9

%N Decimal expansion of the asymptotic mean of the second smallest prime not dividing k, where k runs over the positive integers (A380539).

%F Equals lim_{m->oo} (1/m) * Sum_{k=1..m} A380539(k).

%F Equals Sum_{k>=2} prime(k) * (prime(k)-1) * (primesum(k-1)-k+1) / primorial(k), where primesum(k) = A007504(k) and primorial(k) = A002110(k).

%e 5.15914285965164203013658097450125817200073072141916...

%o (PARI) primorial(k) = prod(i = 1, k, prime(i));

%o primesum(k) = sum(i = 1, k, prime(i));

%o suminf(k = 2, prime(k) * (prime(k)-1) * (primesum(k-1)-k+1) / primorial(k))

%Y Cf. A002110, A007504, A249270 (analogous constant with smallest prime), A380539.

%K nonn,cons,new

%O 1,1

%A _Amiram Eldar_, Feb 14 2025