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A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number , other examples being square numbers and cube numbers . The n th triangular number is the number of dots in the triangular arrangement with n dots on each side, and is equal to the sum of the n natural ...
The infinite sequence of triangular numbers diverges to +∞, so by definition, ... Why –1/12 is a gold nugget follow-up Numberphile video with Edward Frenkel;
← 0 100 200 300 400 500 ... 361 = 19 2. 361 is a centered triangular number, [3] ... number of regions into which a figure made up of a row of 6 adjacent congruent ...
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
199 is a centered triangular number. [1]It is a prime number and the fourth part of a prime quadruplet: 191, 193, 197, 199. [2]199 is the smallest natural number that takes more than two iterations to compute its digital root as a repeated digit sum: + + = + = + = Thus, its additive persistence is three, and it is the smallest number of persistence three.
There are 21 colorings of the four corners of a square using three colors (up to symmetry), a doubly triangular number, formed by combining two of the six colorings of two opposite corners In mathematics, the doubly triangular numbers are the numbers that appear within the sequence of triangular numbers , in positions that are also triangular ...
Each centered triangular number has a remainder of 1 when divided by 3, and the quotient (if positive) is the previous regular triangular number. Each centered triangular number from 10 onwards is the sum of three consecutive regular triangular numbers. For n > 2, the sum of the first n centered triangular numbers is the magic constant for an n ...
← 0 100 200 300 400 500 600 700 800 900 ... 190 is a triangular number, a hexagonal number, and a centered nonagonal number, the fourth figurate number (after 1, ...