Search results
Results from the WOW.Com Content Network
The length of an interval of consecutive integers with property that every element has a factor in common with one of the endpoints. A059756: Sierpinski numbers: 78557, 271129, 271577, 322523, 327739, 482719, 575041, 603713, 903983, 934909, ... Odd k for which { k⋅2 n + 1 : n ∈ } consists only of composite numbers. A076336
The harmonic mean of a set of positive integers is the number of numbers times the reciprocal of the sum of their reciprocals. The optic equation requires the sum of the reciprocals of two positive integers a and b to equal the reciprocal of a third positive integer c. All solutions are given by a = mn + m 2, b = mn + n 2, c = mn.
105 is the 14th triangular number, [1] a dodecagonal number, [2] and the first Zeisel number. [3] It is the first odd sphenic number and is the product of three consecutive prime numbers. 105 is the double factorial of 7. [4] It is also the sum of the first five square pyramidal numbers. 105 comes in the middle of the prime quadruplet (101, 103 ...
In number theory, a polite number is a positive integer that can be written as the sum of two or more consecutive positive integers. A positive integer which is not polite is called impolite . [ 1 ] [ 2 ] The impolite numbers are exactly the powers of two , and the polite numbers are the natural numbers that are not powers of two.
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
Any two consecutive integers have opposite parity. A number (i.e., integer) expressed in the decimal numeral system is even or odd according to whether its last digit is even or odd. That is, if the last digit is 1, 3, 5, 7, or 9, then it is odd; otherwise it is even—as the last digit of any even number is 0, 2, 4, 6, or 8.
If a term is odd, the next term is 3 times the previous term plus 1. The conjecture is that these sequences always reach 1, no matter which positive integer is chosen to start the sequence. The conjecture has been shown to hold for all positive integers up to 2.95 × 10 20 , but no general proof has been found.
Lander, Parkin, and Selfridge conjecture: if the sum of -th powers of positive integers is equal to a different sum of -th powers of positive integers, then +. Lemoine's conjecture : all odd integers greater than 5 {\displaystyle 5} can be represented as the sum of an odd prime number and an even semiprime .