# Keith Number in Java

In this section, we will learn what is Keith number and also create Java programs to check if the given number is Keith or not. The Keith number program frequently asked in Java coding test.

## Keith Number

A positive n digit number X is called a Keith number (or repfigit number) if it is arranged in a special number sequence generated using its digits. The special sequence has first n terms as digits of x and other terms are recursively evaluated as the sum of previous n terms. For example, 197, 19, 742, 1537, etc.

### Keith Number Example

Let's check the number 742 is a Keith number or not.

First, we will separate each digit, as 7, 4, 2

To find the next term of the above-created series, we add these digits (i.e. 7+4+2), and the resultant (13) that we get becomes the next term of the series.

Now, the series becomes, 7, 4, 2, 13

To find the next term of the above series, we add the last three terms (i.e. 13+2+4), and the resultant (19) that we get becomes the next term of the series.

Now, the series becomes, 7, 4, 2, 13, 19

To find the next term of the above series, we add the last three terms (i.e. 19+13+2), and the resultant (34) that we get becomes the next term of the series.

Now, the series becomes, 7, 4, 2, 13, 19, 34

To find the next term of the above series, we add the last three terms (i.e. 34+19+13), and the resultant (66) that we get becomes the next term of the series.

Now, the series becomes, 7, 4, 2, 13, 19, 34, 66

To find the next term of the above series, we add the last three terms (i.e. 66+34+19), and the resultant (119) that we get becomes the next term of the series.

Now, the series becomes, 7, 4, 2, 13, 19, 34, 66, 119

To find the next term of the above series, we add the last three terms (i.e. 119+66+34), and the resultant (219) that we get becomes the next term of the series.

Now, the series becomes, 7, 4, 2, 13, 19, 34, 66, 119, 219

To find the next term of the above series, we add the last three terms (i.e. 219+119+66), and the resultant (404) that we get becomes the next term of the series.

Now, the series becomes, 7, 4, 2, 13, 19, 34, 66, 119, 219, 404

To find the next term of the above series, we add the last three terms (i.e. 404+219+119), and the resultant (742) that we get becomes the next term of the series.

Now, the series becomes, 7, 4, 2, 13, 19, 34, 66, 119, 219, 404, 742

Here, we will stop the process because we get the same number (742) as a term of the series. Hence, the given number 742 is a Keith number.

From the above example, we observe that we need to calculate the terms of the series until we get the same number (that we have taken in starting) as a term of the series.

#### Note: If the given number (X) has n number of digits, we will recursively add the last n terms of the series. As the number 742 has three digits, so, we have added the last three terms of the series, each time.

Let's take another example.

## Steps to Find Keith Number

1. Read or initialize a number (X).
2. Separate each digit from the given number (X).
3. Add all the n-digits. It gives the next term of the series.
4. Again, add the last n-terms of the series to find the next term.
5. Repeat step 4 until we get the term the same as the number we have taken.

Let's implement the above steps in a Java program.

## Keith Number Java Program

The logic is not much difficult. Compute the series using the sum of n previous numbers where n is the number of digits. If one of the numbers computed in the series is the same as the input number, it is a Keith number. The program stops if the value computed is greater than the input number.

Let's create a Java program and implement the above logic into it.

KeithNumberExample1.java

Output:

```Yes, the given number is a Keith number.
Yes, the given number is a Keith number.
No, the given number is not a Keith number.
```

Let's create another Java program to find all the Keith numbers that contain the same number of digits.

KeithNumberExample2.java

Output 1:

Output 2:

Similarly, we can find the d-digit Keith numbers. The following table summarizes the d-digits Keith numbers.

d d-digit Keith Numbers
2 14, 19, 28, 47, 61, 75
3 197, 742
4 1104, 1537, 2208, 2580, 3684, 4788, 7385, 7647, 7909
5 31331, 34285, 34348, 55604, 62662, 86935, 93993
6 120284, 129106, 147640, 156146, 174680, 183186, 298320, 355419, 694280, 925993
7 1084051, 7913837
8 11436171, 33445755, 44121607
9 129572008, 251133297
10 (none)
11 24769286411 96189170155
12 171570159070, 202366307758, 239143607789, 296658839738
13 1934197506555, 8756963649152
14 43520999798747, 74596893730427, 97295849958669
15 120984833091531, 270585509032586, 754788753590897
16 3621344088074041, 3756915124022254, 4362827422508274
17 11812665388886672, 14508137312404344, 16402582054271374, 69953250322018194, 73583709853303061
18 119115440241433462, 166308721919462318, 301273478581322148
19 1362353777290081176, 3389041747878384662, 5710594497265802190, 5776750370944624064, 6195637556095764016
20 12763314479461384279, 27847652577905793413, 45419266414495601903
21 855191324330802397989
22 7657230882259548723593
23 26842994422637112523337, 36899277593852609997403, 61333853602129819189668
24 229146413136585558461227
25 9838678687915198599200604