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 132hard hexagon entropy constant 137139140Stieltjes constant 142pi 144golden ratio 146146151Glaisher-Kinkelin constant 153cube line picking average length155Delian constant 156The probability of the digits of a given real number summing..
An almost integer is a number that is very close to an integer.Surprising examples are given by(1)which equals to within 5 digits and(2)which equals to within 16 digits (M. Trott, pers. comm., Dec. 7, 2004). The first of these comes from the half-angle formula identity(3)where 22 is the numerator of the convergent 22/7 to , so . It therefore follows that any pi approximation gives a near-identity of the form .Another surprising example involving both e andpi is(4)which can also be written as(5)(6)Here, is Gelfond's constant. Applying cosine a few more times gives(7)This curious near-identity was apparently noticed almost simultaneously around 1988 by N. J. A. Sloane, J. H. Conway, and S. Plouffe, but no satisfying explanation as to "why" is true has yet been discovered.Another nested cosine almost integer is given by(8)(P. Rolli, pers. comm., Feb. 19, 2004).An..
The number , where 666 is the beast number and denotes a factorial. The number has approximately decimal digits.The number of trailing zeros in the Leviathan number is(1)(2)(Pickover 1995).
Legion's number of the first kind is defined as(1)(2)where 666 is the beast number. It has 1881 decimaldigits.Legion's number of the second kind is defined as(3)(4)It has approximately digits, and ends with trailing zeros.
Approximations to Khinchin's constant include(1)(2)(3)(4)which are correct to 9, 7, 6, and 5 digits, respectively (M. Hudson, pers. comm., Nov. 20, 2004).