A393949 Decimal expansion of Sum_{p prime} 1/(p*(p+2)) * Product_{p prime} ((1-1/p)^2 * Product_{k>=0} (1 + 2/p^(2^k))).

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

Offset

0,2

Comments

The asymptotic probability that the greatest common infinitary divisor of two positive integers selected independently at random is prime.

Links

Table of n, a(n) for n=0..105.

Formula

Equals A185380 * A393948.

Example

0.193337685331885254963810502573364166897551241064085...

Prog

(PARI) c(m) = prodeulerrat((1 - 1/p)^2 * prod(k = 0, m, 1 + 2/p^(2^k)));
{my(c1 = 0, c2 = 1, m = 1); while(c2 != c1, c1 = c2; c2 = c(m); m++); sumeulerrat(1/(p*(p+2))) * c2}

Crossrefs

Cf. A077609, A185380.

Analogous constants: A222056, A393898.

The asymptotic probability that the greatest common infinitary divisor of two positive integers selected independently at random is: A065472 (square), A393948 (1), this constant (prime), A393950 (squarefree), A393951 (Fermi-Dirac prime), A393952 (exponentially 2^n-number), A393953 (4th power).

Sequence in context: A374752 A138064 A063569 * A037921 A327135 A019878

Adjacent sequences: A393946 A393947 A393948 * A393950 A393951 A393952

Keyword

nonn,cons

Author

Amiram Eldar, Mar 04 2026

Status

approved