Definition

• Two integers are coprime if they share no positive common divisors other than 1.
• a(1) = 1
• a(2) = 2
• a(n) is the smallest positive integer which is coprime to the a(n-1) and a(n-2) and has not yet appeared, for integer n >= 3.

Task

• Given positive integer n, output/print a(n).

Example

• a(11) = 6 because 6 is coprime with the last two predecessors (namely, 11 and 13) and 6 has not appeared before.

Notes

• Note that the sequence is not ascending, meaning that an element can be smaller than its predecessor.

Specs

• You must use 1-indexed.

Testcases

n      a(n)
1      1
2      2
3      3
4      5
5      4
6      7
7      9
8      8
9      11
10     13
11     6
12     17
13     19
14     10
15     21
16     23
17     16
18     15
19     29
20     14
100    139
1000   1355
10000  13387
100000 133361

Scoring

• Since coprime means that the two numbers share only one divisor (1), and 1 is a small number, your code should be as small as possible in terms of byte-count.

References

• OEIS A084937