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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 palindromic number (also known as a numeral palindrome or a numeric palindrome) is a number (such as 16461) that remains the same when its digits are reversed. In other words, it has reflectional symmetry across a vertical axis.
All other four-digit numbers eventually reach 6174 if leading zeros are used to keep the number of digits at 4. For numbers with three identical digits and a fourth digit that is one higher or lower (such as 2111), it is essential to treat 3-digit numbers with a leading zero; for example: 2111 – 1112 = 0999; 9990 – 999 = 8991; 9981 – 1899 ...
The first (base-10) triply palindromic prime is the 11-digit number 10000500001. It is possible that a triply palindromic prime in base 10 may also be palindromic in another base, such as base 2, but it would be highly remarkable if it were also a triply palindromic prime in that base as well.
Any four-digit number (in base 10) with at least two distinct digits will reach 6174 within seven iterations. [1] The algorithm runs on any natural number in any given number base . Definition and properties
4) Penn State The Big Ten runner-up looks to have an easier path to the national championship than the Big Ten champion , a potential flaw to be addressed in the wake of this year's bracket reveal.
Scientists still know very little about the ovaries, but new research and renewed interest suggests unlocking its secrets could help women life longer.
This page provides a list of all articles available at PlanetMath in the following topic: . 11-XX Number theory.. This list will be periodically updated. Each entry in the list has three fields: