A393952 Decimal expansion of Product_{p prime} ((1 + Sum_{k>=0} 1/(p^(2^(k+1)) + 2*p^(2^k))) * (1-1/p)^2 * Product_{k>=0} (1 + 2/p^(2^k))).

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

Offset

0,1

Comments

The asymptotic probability that the greatest common infinitary divisor of two positive integers selected independently at random is an exponentially 2^n-number (A138302).

Links

Table of n, a(n) for n=0..104.

Formula

Equals Product_{p prime} (1 + Sum_{k>=0} 1/(p^(2^(k+1)) + 2*p^(2^k))) * A393948.

Example

0.994380928740398153030200247807975123997755498259925...

Prog

(PARI) c(m) = prodeulerrat(1 + sum(k = 0, m, 1/(p^(2^(k+1)) + 2*p^(2^k)))) * 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++); c2}

Crossrefs

Cf. A077609, A138302.

The asymptotic probability that the greatest common infinitary divisor of two positive integers selected independently at random is: A065472 (square), A393948 (1), A393949 (prime), A393950 (squarefree), A393951 (Fermi-Dirac prime), this constant (exponentially 2^n-number), A393953 (4th power).

Sequence in context: A283749 A249023 A336044 * A382582 A019893 A346585

Adjacent sequences: A393949 A393950 A393951 * A393953 A393954 A393955

Keyword

nonn,cons

Author

Amiram Eldar, Mar 04 2026

Status

approved