511 is the
natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called ''cardinal ...
following
510 and preceding
512
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Year 512 ( DXII) was a leap year starting on Sunday (link will display the full calendar) of the Julian calendar. In the Roman Empire, it was known as the Year of the Consulship of Paulus and Moschianus (or, less frequently, year ...
.
It is a
Mersenne number
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th ...
, being one less than a power of 2:
.
As a result, 511 is a palindromic number and a
repdigit
In recreational mathematics, a repdigit or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The word is a portmanteau of repeated and digit.
Example ...
in bases 2 (111111111
2). It is also palindromic and a repdigit in base 8 (777
8).
It is a generalized
heptagonal number A heptagonal number is a figurate number that is constructed by combining heptagons with ascending size. The ''n''-th heptagonal number is given by the formula
:H_n=\frac.
The first few heptagonal numbers are:
: 0, 1, 7, 18, 34, 55, 81, 112 ...
, since
when
.
It is a
Harshad number in bases 3, 5, 7, 10, 13 and 15.
Special use in computers
The octal representation of 511 (777
8) is commonly used by Unix commands to specify a custom record separator in order to "slurp" input as a whole, rather than line-by-line (i.e. separated at
newline characters).
References
Integers
{{num-stub