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The first nine terms of the sequence 1 2, 11 2, 111 2, 1111 2, ... form the palindromes 1, 121, 12321, 1234321, ... (sequence A002477 in the OEIS) The only known non-palindromic number whose cube is a palindrome is 2201, and it is a conjecture the fourth root of all the palindrome fourth powers are a palindrome with 100000...000001 (10 n + 1).
Pyramid, or pyramid representation, is a type of multi-scale signal representation developed by the computer vision, image processing and signal processing communities, in which a signal or an image is subject to repeated smoothing and subsampling. Pyramid representation is a predecessor to scale-space representation and multiresolution analysis.
For example 111111111111111 (15 digits) is divisible by 111 and 11111 in that base. If a number m can be expressed as a string of prime length to some base, such a number may or may not be prime, but commonly is not; for example, to base 10, there are only three such numbers of length less than 100 (1 is by definition, not prime).
For example: 1 is read off as "one 1" or 11. 11 is read off as "two 1s" or 21. 21 is read off as "one 2, one 1" or 1211. 1211 is read off as "one 1, one 2, two 1s" or 111221. 111221 is read off as "three 1s, two 2s, one 1" or 312211. The look-and-say sequence was analyzed by John Conway [1] after he was introduced to it by one of his students ...
For example, consider the result if we were to union a checkerboard (where every tile is a pixel) of size with its complement. The result is a giant black square which should be represented by a quadtree with just the root node (coloured black), but instead the algorithm produces a full 4-ary tree of depth k {\displaystyle k} .
Geometric representation of the square pyramidal number 1 + 4 + 9 + 16 = 30. In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the stacked spheres in a pyramid with a square base. The study of these numbers goes back to Archimedes and Fibonacci.
Geometric representation of the square pyramidal number 1 + 4 + 9 + 16 = 30. A pyramidal number is the number of points in a pyramid with a polygonal base and triangular sides. [1] The term often refers to square pyramidal numbers, which have a square base with four sides, but it can also refer to a pyramid with any number of sides. [2]
A pyramid with side length 5 contains 35 spheres. Each layer represents one of the first five triangular numbers. A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron.