A number in which the first decimal digits of the fractional part sum to 666 is known as an evil number (Pegg and Lomont 2004).
However, the term "evil" is also used to denote nonnegative integers that have an even number of 1s in their binary expansions, the first few of which are 0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, ... (OEIS A001969), illustrated above as a binary plot. Numbers that are not evil are then known as odious numbers.
Returning to Pegg's definition of evil, the fact that is evil was noted by Keith, while I. Honig (pers. comm., May 9, 2004) noted that the golden ratio is also evil. The following table gives a list of some common evil numbers (Pegg and Lomont 2004).
Ramanujan constant  132 
hard hexagon entropy constant  137 
139  
140  
Stieltjes constant  142 
pi  144 
golden ratio  146 
146  
151  
GlaisherKinkelin constant  153 
cube line picking average length  155 
Delian constant  156 
The probability of the digits of a given real number summing to a relatively large positive integer is roughly given by the number of nonzero digits divided by sum of those digits, namely . Amazingly, the exact probability for summing to a number can be computed exactly using the recursive formulas
(1)
 
(2)

For , 2, ..., the first few values are therefore 1/9, 10/81, 100/739, 1000/6561, ... (OEIS A100061 and A100062; Pegg and Lomont 2004), plotted above.
The generating function for this series is given by
(3)

(Pegg and Lomont 2004). This allows an expression for to be determined in closed form, although it is a complicated expression involving combinations of the algebraic numbers (and polynomial roots) .
For the case of interest (), the result is a rational number having a 635digit numerator and a 636digit denominator that is approximately equal to
(4)

A set of "beastly evil" numbers are given by the following (M. Hudson, pers. comm., Nov 510, 2004).
number  digits 
74  
74  
136  
142  
146  
147  
149  
152  
156  
159  
163  
468  
655  
2018 
Powers of that are evil include , 6, 8, 10, 17, 18, 24, 25, 26, 29, 30, 38, ... (M. Hudson, pers. comm., Nov. 8, 2004).
The analogous problem of terms in a simple continued fraction summing to a given number can also be considered. The following table summarized some constants whose continued fractions have cumulative sums that equal 666 (Pegg and Lomont 2004).
constant  terms 
cube line picking average length  50 
pi  56 
Bloch constant  58 
Gauss's constant  143 
167  
conjectured value of Landau constant  173 
Interestingly, this makes the cube line picking average length and doubly evil.