Golomb Sequence

The Golomb sequence is uniquely defined by the following rules:

1. All terms are positive integers.
2. No term is smaller than any previous term.
3. The nth term is equal to the total number of times that the integer n appears within the sequence.

Write a function that returns the first n terms of the Golomb sequence as a list.

Examples

golomb(1) ➞ [1]

golomb(8) ➞ [1, 2, 2, 3, 3, 4, 4, 4]

golomb(10) ➞ [1, 2, 2, 3, 3, 4, 4, 4, 5, 5]

1 appears once; 2 appears twice; 3 appears twice; 4 appears 3 times; 5 will appear 3 times in the full sequence, etc.

Notes

• The tests will consist of random inputs between 1 and 1000 inclusive.