**1.** Write a Java program to check whether a given number is an ugly number. Go to the editor

In number system, ugly numbers are positive numbers whose only prime factors are 2, 3 or 5. First 10 ugly numbers are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12. By convention, 1 is included.

Test Date:Input an integer number: 235

*Expected Output* :

It is not an ugly number.

**2. ** Write a Java program to classify Abundant, deficient and perfect number (integers) between 1 to 10,000. Go to the editor

In number theory, an abundant number is a number for which the sum of its proper divisors is greater than the number itself.

Example :

The first few abundant numbers are:

12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102,…

The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16.

Deficient number: In number theory, a deficient number is a number n for which the sum of divisors σ(n)<2n, or, equivalently, the sum of proper divisors (or aliquot sum) s(n)<n. The value 2n − σ(n) (or n − s(n)) is called the number's deficiency.

As an example, divisors of 21 are 1, 3 and 7, and their sum is 11. Because 11 is less than 21, the number 21 is deficient. Its deficiency is 2 × 21 − 32 = 10.

The first few deficient numbers are:

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 26, 27, 29, 31, 32, 33, …….

Perfect number: In number system, 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.

Equivalently, a perfect number is a number that is half the sum of all of its positive divisors (including itself) i.e. σ1(n) = 2n.

The first perfect number is 6. Its proper divisors are 1, 2, and 3, and 1 + 2 + 3 = 6. Equivalently, the number 6 is equal to half the sum of all its positive divisors: ( 1 + 2 + 3 + 6 ) / 2 = 6. The next perfect number is 28 = 1 + 2 + 4 + 7 + 14. This is followed by the perfect numbers 496 and 8128.

*Expected Output* :

Number Counting [(integers) between 1 to 10,000]:

Deficient number: 7508

Perfect number: 4

Abundant number: 2488

**3.** Write a Java program to generate random integers in a specific range. Go to the editor

Click me to see the solution

**4.** Write a Java program to generate and show all Kaprekar numbers less than 1000. Go to the editor

*Expected Output* :

1 1 0 + 1 9 81 8 + 1 45 2025 20 + 25 55 3025 30 + 25 99 9801 98 + 01 297 88209 88 + 209 703 494209 494 + 209 999 998001 998 + 001 8 Kaprekar numbers.

**5.** Write a Java program to find the number of seed Lychrel number candidates and related numbers for n in the range 1..10000 inclusive. (With that iteration limit of 500). Go to the editor

A Lychrel number is a natural number that cannot form a palindrome through the iterative process of repeatedly reversing its digits and adding the resulting numbers. This process is sometimes called the 196-algorithm, after the most famous number associated with the process.

The first few Lychrel numbers are 196, 295, 394, 493, 592, 689, 691, 788, 790, 879, 887, ... .

*Expected Output* :

5 Lychrel seeds: [196, 879, 1997, 7059, 9999]

244 Lychrel related

5 Lychrel palindromes: [196, 879, 1997, 7059, 9999]

**6.** Write a Java program to generate and show the first 15 narcissistic decimal numbers. Go to the editor

*Expected Output* :

0 1 2 3 4 5 6 7 8 9 153 370 371 407 1634

**7.** Write a Java program to display first 10 lucus numbers. Go to the editor

The Lucas numbers or series are an integer sequence named after the mathematician François Édouard Anatole Lucas, who studied both that sequence and the closely related Fibonacci numbers. Lucas numbers and Fibonacci numbers form complementary instances of Lucas sequences.

The sequence of Lucas numbers is: 2, 1, 3, 4, 7, 11, 18, 29, ….

*Expected Output* :

First ten Lucas a numbers: 2 1 3 4 7 11 18 29 47 76

**8.**Write a Java program to print out the first 10 Catalan numbers by extracting them from Pascal's triangle. Go to the editor

In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively-defined objects. They are named after the Belgian mathematician Eugène Charles Catalan.

The first Catalan numbers for n = 0, 1, 2, 3, … are 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, 4861946401452,

List 10 Catalan numbers:- 1 2 5 14 42 132 429 1430 4862 16796

**9.** Write a Java program to find and print the first 10 happy numbers. Go to the editor

Happy number: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1, or it loops endlessly in a cycle which does not include 1.

Example: 19 is a happy number

1^{2} + 9^{2}=82

8^{2} + 2^{2}=68

6^{2} + 8^{2}=100

1^{2} + 0^{2} + 0^{2}=1

*Expected Output*

First 10 Happy numbers: 1 7 10 13 19 23 28 31

**10.** Write a Java program to check whether a given number is a happy number or unhappy number. Go to the editor

Happy number: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1, or it loops endlessly in a cycle which does not include 1.

An unhappy number is a number that is not happy.

The first few unhappy numbers are 2, 3, 4, 5, 6, 8, 9, 11, 12, 14, 15, 16, 17, 18, 20.

*Expected Output*

Input a number: 5 Unhappy Number

**11.** Write a Java program to check whether a given number is a Disarium number or unhappy number. Go to the editor

A Disarium number is a number defined by the following process :

Sum of its digits powered with their respective position is equal to the original number.

For example 175 is a Disarium number :

As 1^{1}+3^{2}+5^{3} = 135

Some other DISARIUM are 89, 175, 518 etc.

A number will be called Disarium if the sum of its digits powered with their respective position is equal with the number itself. Sample Input: 135.

*Expected Output*

Input a number : 25 Not a Disarium Number.

**12.** Write a Java program to check whether a number is a Harshad Number or not. Go to the editor

In recreational mathematics, a harshad number in a given number base, is an integer that is divisible by the sum of its digits when written in that base.

Example: Number 200 is a Harshad Number because the sum of digits 2 and 0 and 0 is 2(2+0+0) and 200 is divisible by 2. Number 171 is a Harshad Number because the sum of digits 1 and 7 and 1 is 9(1+7+1) and 171 is divisible by 9.

*Expected Output*

Input a number : 353

353 is not a Harshad Number.

**13.** Write a Java program to check whether a number is a Pronic Number or Heteromecic Number or not. Go to the editor

A pronic number is a number which is the product of two consecutive integers, that is, a number of the form n(n + 1).

The first few pronic numbers are:

0, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420, 462 … etc.

*Expected Output*

Input a number : 110

Pronic Number.

**14.** Write a Java program check whether a number is an Automorphic number or not. Go to the editor

In mathematics, an automorphic number is a number whose square "ends" in the same digits as the number itself. For example, 5^{2} = 25, 6^{2} = 36, 76^{2} = 5776, and 890625^{2} = 793212890625, so 5, 6, 76 and 890625 are all automorphic numbers.

*Expected Output*

Input a number : 76 Automorphic Number.

**15.** Write a Java program to check whether a number is a Duck Number or not. Go to the editor

Note: A Duck number is a number which has zeroes present in it, but there should be no zero present in the beginning of the number. For example 3210, 7056, 8430709 are all duck numbers whereas 08237, 04309 are not.

*Expected Output*

Input a number : 3210 Duck number

**16.** Write a Java program to check two numbers are Amicable numbers or not. Go to the editor

Amicable numbers are two different numbers so related that the sum of the proper divisors of each is equal to the other number.

The first ten amicable pairs are: (220, 284), (1184, 1210), (2620, 2924), (5020, 5564), (6232, 6368), (10744, 10856), (12285, 14595), (17296, 18416), (63020, 76084), and (66928, 66992).

*Expected Output*

Input the first number: 220 Input the second number: 284 These numbers are amicable.

**17.** Write a Java program to check if a given number is circular prime or not. Go to the editor

Circular Prime : A circular prime is a prime number with the property that the number generated at each intermediate step when cyclically permuting its (base 10) digits will be prime.

For example, 1193 is a circular prime, since 1931, 9311 and 3119 all are also prime. A circular prime with at least two digits can only consist of combinations of the digits 1, 3, 7 or 9, because having 0, 2, 4, 6 or 8 as the last digit makes the number divisible by 2, and having 0 or 5 as the last digit makes it divisible by 5.

Input Data:

Input a number: 35

*Expected Output*

It is not a Circular Prime number.

**18.** Write a Java program to check a number is a cube or not. Go to the editor

In arithmetic and algebra, the cube of a number n is its third power: the result of the number multiplied by itself twice:

n^{3} = n × n × n.

Input Data:

Input a number: 8

*Expected Output*

Number is a cube.

**19.** Write a Java program to check a number is a cyclic or not. Go to the editor

A cyclic number is an integer in which cyclic permutations of the digits are successive multiples of the number. The most widely known are 142857:

142857 × 1 = 142857

142857 × 2 = 285714

142857 × 3 = 428571

142857 × 4 = 571428

142857 × 5 = 714285

142857 × 6 = 857142

Input Data:

Input a number: 142857

*Expected Output*

It is a cyclic number.

**20.** Write a Java program to display first 10 Fermat numbers. Go to the editor

In mathematics, a Fermat number is a positive integer of the form

where n is a nonnegative integer.

The first few Fermat numbers are:

3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, …

*Expected Output*

3.0 5.0 17.0 257.0 65537.0 4.294967297E9 1.8446744073709552E19 3.4028236692093846E38 1.157920892373162E77 1.3407807929942597E154 Infinity

**21.** Write java program to find any number between 1 and n that can be expressed as the sum of two cubes in two (or more) different ways. Go to the editor

//http://introcs.cs.princeton.edu/java/13flow/Ramanujan.java.html

Here are some examples of Ramanujan numbers :

1729 = 1^3 + 12^3 = 9^3 + 10^3

* 10000

1729 = 1^3 + 12^3 = 9^3 + 10^3

4104 = 2^3 + 16^3 = 9^3 + 15^3

* 100000

1729 = 1^3 + 12^3 = 9^3 + 10^3

4104 = 2^3 + 16^3 = 9^3 + 15^3

13832 = 2^3 + 24^3 = 18^3 + 20^3

39312 = 2^3 + 34^3 = 15^3 + 33^3

46683 = 3^3 + 36^3 = 27^3 + 30^3

32832 = 4^3 + 32^3 = 18^3 + 30^3

40033 = 9^3 + 34^3 = 16^3 + 33^3

20683 = 10^3 + 27^3 = 19^3 + 24^3

65728 = 12^3 + 40^3 = 31^3 + 33^3

64232 = 17^3 + 39^3 = 26^3 + 36^3

1729 = 1^3 + 12^3 = 9^3 + 10^3 4104 = 2^3 + 16^3 = 9^3 + 15^3 13832 = 2^3 + 24^3 = 18^3 + 20^3 39312 = 2^3 + 34^3 = 15^3 + 33^3 46683 = 3^3 + 36^3 = 27^3 + 30^3 32832 = 4^3 + 32^3 = 18^3 + 30^3 40033 = 9^3 + 34^3 = 16^3 + 33^3 20683 = 10^3 + 27^3 = 19^3 + 24^3 65728 = 12^3 + 40^3 = 31^3 + 33^3 64232 = 17^3 + 39^3 = 26^3 + 36^3

**22.** Write a program to check if a number is Mersenne number or not. Go to the editor

In mathematics, a Mersenne number is a prime number that can be written in the form Mn = 2n − 1 for some integer n.

The first four Mersenne primes are 3, 7, 31, and 127

Input a number: 127 127 is a Mersenne number.

**23.** Write a Java program to find all the narcissistic numbers between 1 and 1000. Go to the editor

In number theory, a narcissistic number is a number that is the sum of its own digits each raised to the power of the number of digits.

For example:

153 = 1^{3} + 5^{3} + 3^{3}

1 2 3 4 5 6 7 8 9 153 370 371 407

**24.** Write a Java program to check if a number is palindrome or not. Go to the editor

In number system a palindromic number is a number that is the same when written forwards or backwards, i.e., of the form .

The first few palindromic numbers are therefore are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, …

Input a number: 5 It is a Palindrome number.

**25.** Write a Java program to print the first 15 numbers of the Pell series. Go to the editor

In Pell series the first two numbers in the sequence are both 2, and each successive number is formed by adding twice the previous Pell–Lucas number to the Pell–Lucas number before that, or equivalently, by adding the next Pell number to the previous Pell number:

thus, 82 is the companion to 29, and 82 = 2 × 34 + 14 = 70 + 12.

The first few terms of the sequence are :

0, 1, 2, 5, 12, 29, 70, 169, 408, 985, 2378, 5741, 13860,…

First 20 Pell numbers: 1 2 5 12 29 70 169 408 985 2378 5741 13860 33461 80782 195025 470832 113 6689 2744210 6625109 15994428

**26.** Write a Program in Java to check whether a number is a Keith Number or not. Go to the editor

In recreational mathematics, a Keith number or repfigit number (short for repetitive Fibonacci-like digit) is a number in the following integer sequence:

14, 19, 28, 47, 61, 75, 197, 742, 1104, 1537, 2208, 2580, 3684, 4788, 7385, 7647, 7909, 31331, 34285, 34348, 55604, 62662, 86935, 93993, 120284, 129106, 147640, 156146, 174680, 183186, 298320, 355419, 694280, 925993,

Input a number: 75 Keith Number

**27.** Write a Java program to check if a given number is circular prime or not. Go to the editor

A circular prime is a prime number with the property that the number generated at each intermediate step when cyclically permuting its (base 10) digits will be prime.

For example, 1193 is a circular prime,

since 1931, 9311 and 3119 all are also prime.

A circular prime with at least two digits can only consist of combinations of the digits 1, 3, 7 or 9, because having 0, 2, 4, 6 or 8 as the last digit makes the number divisible by 2, and having 0 or 5 as the last digit makes it divisible by 5

Input a number: 1193 Output: 1193 1931 9311 3119 1193 is a circular_num Prime number.

**28.** Write a Java program to create the first twenty Hamming numbers. Go to the editor

In computer science, regular numbers are often called Hamming numbers, Hamming Numbers are numbers whose only prime factors are 2, 3 and 5.

The first few hamming numbers are :

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32

First Twenty Hamming numbers: 1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 27 30 32 36

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