Stern-Brocot sequence

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For this task, the Stern-Brocot sequence is to be generated by an algorithm similar to that employed in generating the Fibonacci sequence.

1. The first and second members of the sequence are both 1:

• 1, 1

3. Start by considering the second member of the sequence
4. Sum the considered member of the sequence and its precedent, (1 + 1) = 2, and append it to the end of the sequence:

• 1, 1, 2

6. Append the considered member of the sequence to the end of the sequence:

• 1, 1, 2, 1

8. Consider the next member of the series, (the third member i.e. 2)
9. GOTO 3

• ─── Expanding another loop we get: ───

11. Sum the considered member of the sequence and its precedent, (2 + 1) = 3, and append it to the end of the sequence:

• 1, 1, 2, 1, 3

13. Append the considered member of the sequence to the end of the sequence:

• 1, 1, 2, 1, 3, 2

15. Consider the next member of the series, (the fourth member i.e. 1)