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In number theory, a narcissistic number [1] [2] (also known as a pluperfect digital invariant (PPDI), [3] an Armstrong number [4] (after Michael F. Armstrong) [5] or a plus perfect number) [6] in a given number base is a number that is the sum of its own digits each raised to the power of the number of digits.
A number that is non-palindromic in all bases b in the range 2 ≤ b ≤ n − 2 can be called a strictly non-palindromic number. For example, the number 6 is written as "110" in base 2, "20" in base 3, and "12" in base 4, none of which are palindromes. All strictly non-palindromic numbers larger than 6 are prime.
This is a list of recreational number theory topics (see number theory, recreational mathematics). Listing here is not pejorative : many famous topics in number theory have origins in challenging problems posed purely for their own sake.
For example, p = 10 11310 + 4661664 × 10 5652 + 1, which has q = 11311 digits, and 11311 has r = 5 digits. The first (base-10) triply palindromic prime is the 11-digit number 10000500001. The first (base-10) triply palindromic prime is the 11-digit number 10000500001.
For example, the constant π may be defined as the ratio of the length of a circle's circumference to its diameter. The following list includes a decimal expansion and set containing each number, ordered by year of discovery. The column headings may be clicked to sort the table alphabetically, by decimal value, or by set.
Quinary (base 5 or pental [1] [2] [3]) is a numeral system with five as the base.A possible origination of a quinary system is that there are five digits on either hand.. In the quinary place system, five numerals, from 0 to 4, are used to represent any real number.
3. Keebler Fudge Magic Middles. Neither the chocolate fudge cream inside a shortbread cookie nor versions with peanut butter or chocolate chip crusts survived.
Let be a natural number. For a base >, we define the sum of the factorials of the digits [5] [6] of , :, to be the following: = =!. where = ⌊ ⌋ + is the number of digits in the number in base , ! is the factorial of and
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