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Articles by Rinish Patidar
54 articles
Centered Pentadecagonal Number
The problem includes printing the N-th centered pentadecagonal number for any input number N. A centered pentadecagonal number is a number that can be represented in the form of a figure with a dot in the centre and surrounded by successive layers of the pentadecagon i.e. 15-sided polygon. Here the successive layers of the pentadecagon depict that the first layer surrounding the dot in the centre will be 15-sided polygon, the next layer will be 30-sided polygon followed by a 45-sided polygon and so on. We can understand the concept of centered pentadecagonal with the below figures. The first ...
Read MoreCentered Octagonal Number
The problem statement includes printing the N-th centered octagonal number for some positive integer N, which will be given by the user. A centered octagonal number is a type of number which can be represented in a pattern of figures. Every centered octagonal number can be represented as a dot in the centre surrounded by the successive layers of an Octagon. An octagon is a type of polygon in geometry which has 8 sides in it. The successive layers of an octagon means that the first layer surrounding the dot in the centre will be an octagon, the second ...
Read MoreCentered Octadecagonal Number
The problem includes to print the N-th centered octadecagonal number, where N will be given as an input. A centered octadecagonal number is a type of figurative number which is represented as a dot in the centre surrounded by the successive layers of the octadecagon. An octadecagon is a polygon with 18 sides in it. The successive layers of the octadecagon are the first layer will be 18-sided polygon, the next will be 36-sided polygon and so on. The numbers can be better explained with the help of figures. The first number is represented as a dot in the ...
Read MoreCentered nonadecagonal number
The problem statement includes printing of the N-th centered nonadecagonal number for any positive value of N. A centered nonadecagonal numbers are numbers which are represented in a particular pattern of figure. This number can be represented in a figure as a dot in the centre surrounded by the successive layers of the nonadecagon. A nonadecagon is a type of polygon in mathematics which has 19 sides in it. The successive layers of the nonadecagon suggests that the first layer surrounding the dot in the centre will be 19 sided polygon followed by 38 sided polygon and so ...
Read MoreCentered dodecahedral number
The problem statement says to print the N-th centered dodecahedral number for any positive value of N which will be the user input. A centered dodecahedral number is a number that can be represented in a particular pattern of figure. A dodecahedron is a three-dimensional figure in mathematics which has 12 flat faces. And a centered dodecahedral number is a number which can be represented in the form of a figure with a dot in the centre surrounded by the successive layers of the dodecahedron (12 faced 3-d structure). The successive layers of the dodecahedron says the first layer will ...
Read MoreCentered cube number
The problem statement includes printing the N-th centered cube number for some positive value of N, which will be the user input. A centered cube number is the number of points in a three-dimensional pattern created by a point surrounded by concentric cubical layers of points, with i^2 points on the square faces of the ith layer. It is equivalently the number of points in a body-centered cubic pattern within the cube with n + 1 points along each of its edges. You can refer to wikipedia for figurative representation of the centered cube number which will help in better ...
Read MoreOdd numbers in N-th row of Pascal’s Triangle
The problem statement includes counting the odd numbers in N−th row of Pascal’s triangle. A pascal’s triangle is a triangular array where each row represents the binomial coefficients in the expansion of binomial expression. The Pascal’s triangle is demonstrated as below: 1 1 ...
Read MoreMoser-de Bruijn Sequence
The problem statement includes printing the first N terms of the Moser−de Bruijn Sequence where N will be given in the user input. The Moser−de Bruijn sequence is a sequence consisting of integers which are nothing but the sum of the different powers of 4 i.e. 1, 4, 16, 64 and so on. The first few numbers of the sequence include 0, 1, 4, 5, 16, 17, 20, 21, 64....... The sequence always starts with zero followed by the sum of different powers of 4 such as $\mathrm{4^{0}}$ i.e $\mathrm{4^{1}\:i.e\:4, }$ then sum of $\mathrm{4^{0}\:and\:4^{1}\:i.e\:5}$ and so on. In this ...
Read MoreVantieghems Theorem for Primality Test
The problem statement includes using Vantieghems theorem for primality test i.e. we will check for a positive number N which will be user input and print if the number is a prime number or not using the Vantieghems theorem. Vantieghem’s Theorem The Vantieghems theorem for primality states that a positive number, N is a prime number if the product of $\mathrm{2^{i}−1}$ where the value of i ranges from 1 to N−1 is congruent to N modulo $\mathrm{2^{N}−1}$ If both the values are congruent then the number N is a prime number else it is not a prime number. Congruent ...
Read MoreSum of Range in a Series of First Odd then Even Natural Numbers
The problem statement includes finding the sum of range in a series of first odd numbers then even natural numbers up to N. The sequence consists of all the odd natural numbers from 1 to N and then all the even natural numbers from 2 to N, including N. The sequence will be of size N. We will be provided with a range in the problem for which we need to find out the sum of the sequence within that range, a and b i.e. [a, b]. Here a and b are included in the range. For example, we are ...
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