A394009 Decimal expansion of Product_{p prime} (1-1/p)^2 * (1 + 2 * Sum_{k >= 0} 1/p^(2^k)).

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

Offset

0,1

Comments

The asymptotic probability that two positive integers selected independently at random are coprime and both are exponentially 2^n numbers (A138302).

Links

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

Formula

Equals A271727^2 * A394010.

Example

0.500993677671021447977570913356513912901140108067308...

Prog

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

Crossrefs

Cf. A138302, A271727, A394002, A394006, A394010.

Sequence in context: A198225 A256929 A068459 * A099222 A341796 A340481

Adjacent sequences: A394006 A394007 A394008 * A394010 A394011 A394012

Keyword

nonn,cons

Author

Amiram Eldar, Mar 06 2026

Status

approved