Numbers and its Specialities

NUMBERS-SPECIALITY

Automorphic number :

An automorphic number is a number which is present in the last digit(s) of its square. Example: 25 is an automorphic number as its square is 625 and 25 is present as the last digits.

Neon number:

A number is said to be a Neon Number if the sum of digits of the square of the number is equal to thenumber itself. Example 9 is a Neon Number. 9*9=81 and 8+1=9.Hence it is a Neon Number.

Magic number :

A number is said to be a Magic number if the sum of its digits are calculated till a single digit is obtained by recursively adding the sum of its digits. If the single digit comes to be 1 then the number is a magic number.

Example :

901

9+0+1=10

1+0=1

Palindrome:

Reverse of a number is also same as the original number.

Examle:

100001,

123454321.

 Taxicab number:

In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), also called the nth Hardy–Ramanujan number, is defined as the smallest number that can be expressed as a sum of two positive cube numbers in n distinct ways. The most famous taxicab number is 1729 = Ta(2) = 13 + 123 = 93 + 103.

Armstrong number:

A positive integer is called an Armstrong number of order n if abcd… = an + bn + cn + dn + … In case of an Armstrong number of 3 digits, the sum of cubes of each digits is equal to the number itself. For example: 153 = 1*1*1 + 5*5*5 + 3*3*3 // 153 is an Armstrong number.

Strong number:

If the sum of factorial of the digits in any number is equal the given number then the number is called as STRONG number.

Ex=1! +4! +5!= 1+24+120 = 145

Perfect Number:

In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself

Ex:    6      (1,2,3,6 sum of divisors excluding itself=1+2+3=6)

Happy number:

happy number is a number defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number either equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers, while those that do not end in 1 are unhappy numbers (or sad numbers).

happy-number

Is 1634 a armstrong number?

Pick the strong number:

Pick the armstrong number:

Pick the happy number:

Pick the perfect number

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