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Sociable Dudeney numbers and amicable Dudeney numbers are the powers of their respective roots. The number of iterations i {\displaystyle i} needed for F p , b i ( n ) {\displaystyle F_{p,b}^{i}(n)} to reach a fixed point is the Dudeney function's persistence of n {\displaystyle n} , and undefined if it never reaches a fixed point.
Fifty is the smallest number that is the sum of two non-zero square numbers in two distinct ways. [ 1 ] 50 is a Stirling number of the first kind and a Narayana number . Look up fifty in Wiktionary, the free dictionary.
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Cubesort is a parallel sorting algorithm that builds a self-balancing multi-dimensional array from the keys to be sorted. As the axes are of similar length the structure resembles a cube.
A Cabtaxi number is the smallest positive number that can be expressed as a sum of two integer cubes in n ways, allowing the cubes to be negative or zero as well as positive. The smallest cabtaxi number after Cabtaxi(1) = 0, is Cabtaxi(2) = 91, [ 5 ] expressed as:
NumPy (pronounced / ˈ n ʌ m p aɪ / NUM-py) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. [3]
A more restrictive taxicab problem requires that the taxicab number be cubefree, which means that it is not divisible by any cube other than 1 3. When a cubefree taxicab number T is written as T = x 3 + y 3, the numbers x and y must be relatively prime. Among the taxicab numbers Ta(n) listed above, only Ta(1) and Ta(2) are cubefree
When a triple of numbers a, b and c forms a primitive Pythagorean triple, then (c minus the even leg) and one-half of (c minus the odd leg) are both perfect squares; however this is not a sufficient condition, as the numbers {1, 8, 9} pass the perfect squares test but are not a Pythagorean triple since 1 2 + 8 2 ≠ 9 2.