Category Archives: Mathematical

Carol Number

A Carol number is an integer of the form 4n – 2(n+1) – 1. An equivalent formula is (2n-1)2 – 2. An Interesting Property : For n > 2, the binary representation of the n-th Carol number is n-2 consecutive one’s, a single zero in the middle, and n + 1 more consecutive one’s. Example,… Read More »

Emirp numbers

Emirp is the word “prime” spelled backwards, and it refers to a prime number that becomes a new prime number when you reverse its digits. Emirps do not include palindromic primes (like 151 or 787) nor 1-digit primes like 7. 107, 113, 149, and 157 – reverse them and you’ve got a new prime number… Read More »

Abundant Number

A number n is said to be Abundant Number if sum of all the proper divisors of the number denoted by sum(n) is greater than the value of the number n. And the difference between these two values is called the abundance. Mathematically, if below condition holds the number is said to be Abundant number:… Read More »

Hexagonal Number

Given an integer n, the task is to find the n’th hexagonal number . The n’th hexagonal number Hn is the number of distinct dots in a pattern of dots consisting of the outlines of regular hexagons with sides up to n dots, when the hexagons are overlaid so that they share one vertex.{Source :… Read More »

Powerful Number

A number n is said to be Powerful Number if for every prime factor p of it, p2 also divides it. For example:- 36 is a powerful number. It is divisible by both 3 and square of 3 i.e, 9. The first few Powerful Numbers are: 1, 4, 8, 9, 16, 25, 27, 32, 36,… Read More »

Padovan Sequence

Padovan Sequence similar to Fibonacci sequence with similar recursive structure. The recursive formula is, P(n) = P(n-2) + P(n-3) P(0) = P(1) = P(2) = 1 Fibonacci Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…… Spiral of squares with side lengths which follow the Fibonacci sequence. Image Source : https://en.wikipedia.org/wiki/Fibonacci_number Padovan… Read More »

Juggler Sequence

Juggler Sequence is a series of integer number in which the first term starts with a positive integer number a and the remaining terms are generated from the immediate previous term using the below recurrence relation: Juggler Sequence starting with number 3: 5, 11, 36, 6, 2, 1 Juggler Sequence starting with number 9: 9,… Read More »

Deficient Number

A number n is said to be Deficient Number if sum of all the divisors of the number denoted by divisorsSum(n) is less than twice the value of the number n. And the difference between these two values is called the deficiency. Mathematically, if below condition holds the number is said to be Deficient: divisorsSum(n)… Read More »