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The RATS Sequence


In Mathematics, one of the amazing concepts is the Reverse-Add-Then-Sort (RATS) Sequence.

The RATS Sequence is a sequence that is formed by reversing, adding, then sorting the digits.

Let's understand this concept in detail:

Form the RATS Sequence

Step 1: Consider any number (must be greater than 0).

Step 2: Reverse the number.

Step 3: Add the original number (considered in Step 1) with the number formed by reversing the number (in Step 2).

Step 4: Sort the number obtained in Step 3 in ascending order. The resultant obtained after sorting the number forms the next sequence after n iteration.

Examples

First Iteration

Step 1: Number 1.

Step 2: Reversing the number 1 gives the resultant 1.

Step 3: Adding the original number 1 (considered in Step 1) with the number formed by reversing (in Step 2)  i.e. 1 gives the resultant 2.

Step 4: Sorting the number obtained in Step 3 in ascending order gives the resultant 2. Here number 2 forms the next sequence after the first iteration as shown below:

The sequence is: 1, 2, .....

Second Iteration

Step 1: Number 2.

Step 2: Reversing the number 2 gives the resultant 2.

Step 3: Adding the original number 2 (considered in Step 1) with the number formed by reversing (in Step 2)  i.e. 2 gives the resultant 4.

Step 4: Sorting the number obtained in Step 3 in ascending order gives the resultant 4. Here number 4 forms the next sequence after the second iteration as shown below:

The sequence is: 1, 2, 4, .....

Third Iteration

Step 1: Number 4.

Step 2: Reversing the number 4 gives the resultant 4.

Step 3: Adding the original number 4 (considered in Step 1) with the number formed by reversing (in Step 2)  i.e. 4 gives the resultant 8.

Step 4: Sorting the number obtained in Step 3 in ascending order gives the resultant 8. Here number 8 forms the next sequence after the third iteration as shown below:

The sequence is: 1, 2, 4, 8, .....

Fourth Iteration

Step 1: Number 8.

Step 2: Reversing the number 8 gives the resultant 8.

Step 3: Adding the original number 8 (considered in Step 1) with the number formed by reversing (in Step 2)  i.e. 8 gives the resultant 16.

Step 4: Sorting the number obtained in Step 3 in ascending order gives the resultant 16. Here number 16 forms the next sequence after the fourth iteration as shown below:

The sequence is: 1, 2, 4, 8, 16, .....

Fifth Iteration

Step 1: Number 16.

Step 2: Reversing the number 16 gives the resultant 61.

Step 3: Adding the original number 16 (considered in Step 1) with the number formed by reversing (in Step 2)  i.e. 61 gives the resultant 77.

Step 4: Sorting the number obtained in Step 3 in ascending order gives the resultant 77. Here number 77 forms the next sequence after the fifth iteration as shown below:

The sequence is: 1, 2, 4, 8, 16, 77, .....

Sixth Iteration

Step 1: Number 77.

Step 2: Reversing the number 77 gives the resultant 77.

Step 3: Adding the original number 77 (considered in Step 1) with the number formed by reversing (in Step 2)  i.e. 77 gives the resultant 154.

Step 4: Sorting the number obtained in Step 3 in ascending order gives the resultant 145. Here number 145 forms the next sequence after the sixth iteration as shown below:

The sequence is: 1, 2, 4, 8, 16, 77, 145, .....

Seventh Iteration

Step 1: Number 145.

Step 2: Reversing the number 145 gives the resultant 541.

Step 3: Adding the original number 145 (considered in Step 1) with the number formed by reversing (in Step 2)  i.e. 541 gives the resultant 686.

Step 4: Sorting the number obtained in Step 3 in ascending order gives the resultant 668. Here number 668 forms the next sequence after the seventh iteration as shown below:

The sequence is: 1, 2, 4, 8, 16, 77, 145, 668, .....

Hope you have understood this amazing concept of the RATS Sequence. You may try yourself using the number 668 from the above sequence and form the next sequence. In case of any query, please feel free to provide your valuable comments.
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