A117493 - OEIS

%I #2 Mar 30 2012 17:36:43

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

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

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

%N Decimal expansion of limit as n -> infinity of {1/2 ^ 1/3 ^ 1/5 ^ ... ^ 1/prime(2n)}.

%C This is the upper limit (limit superior) as m -> infinity of the sequence of real numbers 1/2, 1/2 ^ 1/3, 1/2 ^ 1/3 ^ 1/5, ..., 1/2 ^ 1/3 ^ 1/5 ^ ... ^ 1/prime(m). The sequence oscillates. A117492 gives the lower limit.

%e 0.71940503124509211880908153356476875...

%o (PARI) /* Call procedure with large even value for m */ a(m) = r=1/prime(m); forstep(k=m-1,1,-1, r=(1/prime(k))^r); r

%Y Cf. A117492.

%K cons,nonn

%O 0,1

%A _Rick L. Shepherd_, Mar 22 2006