The Amazing Concepts

One of the amazing concepts associated with the numbers is multiplication with three and adding the resultant digits. As per this amazing concept, if any number is multiplied with three and the resultant digits are added all together, then the new resultant digits are divisible by three. The Concept Step 1: Take any number. Step 2: Multiply the number (taken in Step 1) with three. Step 3: Add the resultant digits (obtained in Step 2) all together. Step 4: The new resultant formed in Step 3 is divisible by three. For Example Number 15 Multiply the number with three: 15 x 3 => 45. Add the resultant digits: 4 + 5 => 9. The new resultant is divisible by three: 9 / 3 => 3. Number 25 Multiply the number with three: 25 x 3 => 75. Add the resultant digits: 7 + 5 => 12. The new resultant is divisible by three: 12 / 3 => 4. Number 99 Multiply the number with three: 99 x 3 => 297. Add the resultant digits: 2 + 9 + 7 => 18. The new resu...

Pronic number, also known as Oblong number, Heteromecic number, or Rectangular number, is a positive integer n which is the product of two consecutive integers. Pronic Number Formula Pronic number formula is given below: n (n + 1) Pronic Number Sequence 0, 2, 6, 12, 20, 30, 42, ….., n. For Example Integer : 56 For integer 56, the value of first consecutive integer = 7. Putting this value of first consecutive integer in Pronic number formula: 7 (7 + 1) => 7 x 8 => 56. Integer : 72 For integer 72, the value of first consecutive integer = 8. Putting this value of first consecutive integer in Pronic number formula: 8 (8 + 1) => 8 x 9 => 72. Integer : 110 For integer 110, the value of first consecutive integer = 10. Putting this value of first consecutive integer in Pronic number formula: 10 (10 + 1) => 10 x 11 => 110. Integer : 156 For integer 156, the value of first consecutive integer = 12. Putting this value of first consecu...

In number theory, a Practical number or Panarithmic number is a positive integer n that can represent all smaller numbers m (m < n) as the sums of distinct divisors of n. In other words, any positive integer n having the property that all smaller integers can be represented as the sums of distinct divisors of integer n is referred to as a Practical number or Panarithmic number. The Procedure Step 1:  Consider a positive integer n. Step 2:  Find out the distinct divisors of n. Step 3:  Check whether all numbers smaller than n can be represented as the sums of distinct divisors of n. Step 4:  If all numbers smaller than n can be represented as the sums of distinct divisors of n, then n is a Practical number or Panarithmic number, else not. Practical Number Sequence 1, 2, 4, 6, 8, 12, 16, 18, 20, ….., n. For Example Integer: 24 Distinct divisors of 24: 1, 2, 3, 4, 6, 8, 12. All smaller numbers such as: 5 => 2 + 3 7 => 3 + 4 9 =>...

The Catalan numbers are a sequence of positive integers that occur in numerous counting problems as far as the combinatorics (the branch of mathematics concerned with counting) is concerned. The Catalan numbers are named after the Belgian mathematician Eugene Charles Catalan [30 May, 1814 – 14 February, 1894]. Below is the formula for finding the Catalan numbers: where n is an integer = 0, 1, 2, 3, 4, 5, 6, 7, ………., n-times. Catalan numbers formula The first few Catalan numbers for different values of integer n are shown below: C 0 = 1. C 1 = 1. C 2 = 2. C 3 = 5. C 4 = 14. C 5 = 42. Hope you have understood this amazing concept of  Catalan numbers. In case of any issue, provide your valuable comments.

This post is about amazing facts which may not be known to you before reading here. So let’s start about these amazing facts: Fact 1: Every odd number contains the letter “e” in it. Fact 2: The only number spelt with letters arranged in alphabetical or ascending order is “forty”. Fact 3: The only number spelt with letters arranged in descending order is “one”. Fact 4: Obelus is the symbol for division. Fact 5: The only number from 0 to 1000 that contains the letter e in it is “one thousand”. Fact 6: 1/100 th part of a second is called jiffy. Fact 7: Temperature -40 o C is equal to -40 o F. [C = Celsius, F = Fahrenheit]. Fact 8: 2 is the only even prime number. Fact 9: Pythagoras’ constant 1.141 is the square root of 2. Fact 10: The only number that cannot be represented in Roma numerals is zero. Fact 11: 6 weeks = 10! seconds. [Proof: 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800 seconds = 60,480 minutes = 1,008 hours = 42 days = 6 weeks]. Fact 12: 111,1...

The concept of Self number or Devlali number or Colombian number was introduced by D. R. Kaprekar (Dattatreya Ramchandra Kaprekar). Self number or Devlali number or Colombian number is an integer that cannot be expressed as the sum of any other integer and its individual digits. In other words, if any integer y cannot be expressed as the sum of any other integer n and its individual digits, then it is referred to as Self number or Devlali number or Colombian number. Important Points Point 1: All integer n less than 15 give the result less than 20. Point 2: All integer n greater than or equal to 15 give the result greater than 20. The Procedure Step 1: Consider an integer y. Step 2: Take any other integer n. Step 3: Add integer n with its individual digits. Step 4: If the sum is not equal to the original integer y taken in Step 1, then integer y is Self number or Devlali number or Colombian number, else not. For Example Integer y: 20 Take any other integer: 1...

D. R. Kaprekar (Dattatreya Ramchandra Kaprekar) introduced an amazing concept Kaprekar number in number theory. Kaprekar number is a natural number whose square when divided into two equal or non-equal parts; left and right, then the sum of both parts must be equal to the original number. None of the parts should have the value zero. The Procedure Step 1: Consider a natural number n. Step 2: Square the number n 2 . Step 3: Divide the value after square into two equal or non-equal parts: left x or x-1 digits and right y digits. Step 4: Add both left and right parts: (x + y) or (x-1 + y). Step 5: If the resultant z is equal to the original number n, then number n is a Kaprekar number, else not. For Example Number n: 9 Square the number n 2 : 9 2 => 81. Divide the value after square into two equal or non-equal parts: 8 and 1. Add both left and right parts: 8 + 1=> 9. Here the resultant 9 is equal to the original number n. Hence, 9 is a Kaprekar number. ...