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

Author

Amiram Eldar, Feb 14 2025

Keywords

• nonn
• cons

Examples

			5.15914285965164203013658097450125817200073072141916...
		

Crossrefs

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

Programs

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))

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).