%I #6 Apr 12 2014 16:27:36

%S 2,1,1,1,3,9,3,0,1,1,16,25,8,3,32,32,37,24,53,17,28,67,52,2,21,81,56,

%T 88,9,3,80,42,15,37,107,52,32,120,49,46,84,3,129,29,159,103,90,172,

%U 128,98,202,138,207,150,249,131,132,66,9,86,137,191,236,141,222,285,8,205,310,250,63,173,288,93,294,84,66,104,28,154,93,229,96,254,333,89,126,393,388,396,418,424,356,299,482,64,114,60,513,471

%N Primorial expansion of e.

%C The primorial expansion a(n) of a real number x is defined as x = a(0) + sum(i>0, a(i) / prime(i)# ) where a(0) = floor(x) and 0 <= a(i) < prime(i) for all i > 0.

%F x(0) = e;

%F a(n) = floor(x(n));

%F x(n + 1) = prime(n) * (x(n) - a(n));

%F where prime(n) = A000040(n) is the n-th prime number.

%F a(n) gives the primorial expansion of x(0) = e.

%e e = 2 + 1/prime(1)# + 1/prime(2)# + 1/prime(3)# + 3/prime(4)# + 9/prime(5)# + ...

%e where prime(n)# = A002110(n) is the n-th primorial.

%t pe = Block[{x = #, $MaxExtraPrecision = \[Infinity]},

%t Do[x = Prime[i] (x - Sow[x // Floor]) // Expand, {i, #2 - 1}];

%t x // Floor // Sow] // Reap // Last // Last // Function;

%t pe[E, 100]

%K nonn

%O 0,1

%A _Albert Lau_, Apr 06 2014