A394009 - OEIS

%I #4 Mar 06 2026 14:49:49

%S 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,

%T 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,

%U 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

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

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

%F Equals A271727^2 * A394010.

%e 0.500993677671021447977570913356513912901140108067308...

%o (PARI) c(m) = prodeulerrat((1-1/p)^2 * (1 + 2 * sum(k = 0, m, 1/p^(2^k))));

%o {my(c1 = 0, c2 = 1, m = 1); while(c2 != c1, c1 = c2; c2 = c(m); m++); c2}

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

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, Mar 06 2026