A381113 Decimal expansion of the asymptotic mean of the second smallest prime not dividing k, where k runs over the positive integers (A380539).

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, 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, 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

Offset

1,1

Links

Table of n, a(n) for n=1..105.

Formula

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

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).

Example

5.15914285965164203013658097450125817200073072141916...

Prog

(PARI) primorial(k) = prod(i = 1, k, prime(i));
primesum(k) = sum(i = 1, k, prime(i));
suminf(k = 2, prime(k) * (prime(k)-1) * (primesum(k-1)-k+1) / primorial(k))

Crossrefs

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

Sequence in context: A120283 A103986 A196404 * A128359 A340213 A170903

Adjacent sequences: A381108 A381110 A381111 * A381115 A381116 A381117

Keyword

nonn,cons,new

Author

Amiram Eldar, Feb 14 2025

Status

approved