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The Golomb Sequence is named after Solomon w. Golomb. Solomon Wolf Golomb was an American mathematician and engineer.

He worked as a professor at the University of Southern California. He was best known for his mathematical games. The sequence is also called Silverman’s Sequence.

## Introduction Golomb Sequence

Golomb Sequence can be defined as: –

The Sequence is a non-decreasing (no element is less than the element before; in simple words, we can say that every element is greater than or equal to the one before it) integer sequence where the n-th term is equal to several times n appears in the sequence.

The first few values of the Golomb’s Sequence are: –
1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, ……

Let us know the explanation of these terms: –

• The first term is 1, and one appears 1 time.
• The second term is 2, and two appear 2 times.
• The third term is 2, and three appears 2 times.
• The fourth term is 3, and four appears 3 times
• And so on………………………………………………………

## Examples on Golomb Sequence

Now, we will solve questions related to the Golomb’s sequence: –

### Example 1:

A positive integer n is given to you. Do you have to find the first n terms of the Golomb’s sequence?

Case 1 = If n is 3, which means
Input = 3
The output will be, or the first n terms of the sequence will be 1,2,2.

Case 2 = If n is 7, which means
Input = 7
The output will be, or the first n terms of the sequence will be 1,2,2,3,3,4,4,4,5,5,5.

### Example 2:

If the Sixth term of a Golomb sequence is 4, how many times will 6 appear in the sequence?

Write the Sequence first: – 1,2,2,3,3,4,4,4,5,5,5…………….
If the sixth term is 4, six will appear four times in the sequence.

Golomb Sequence: – 1,2,2,3,3,4,4,4,5,5,5,6,6,6,6………………….

## Practice

1. A positive integer n = 6 is given to you; what will be the first n terms of the Golomb sequence?
2. If the fourth term of a Golomb’s sequence is 3, how many times will 4 appear in the Golomb sequence?