Morning everyone,

Bit of background, I'm a mid level programmer with very limited mathematics skills. As part of an assessment for a new role I've been asked to complete a technical task which mirrors the title of this question.

The programming side is fine yet it is the mathematics side of things that have confused me. We have been given a sample output to replicate(see below).

**Fibonacci:** 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610

**Lucas:** 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843

**Phi Rounded:** 2, 2, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843

Now where I come unstuck, I understand how Fibonacci and Lucas work and the sequence begins but it is the rounded Phi sequence that confuses me. From 3 onwards it seems to generate the next number like the previous 2. It is the beginning of 2,2 that confuses me. Obviously Phi rounded is 2 so how is the second 2 generated in this sequence? Is there a rule that I am missing?

Any help would be greatly appreciated.

We have been told to assume Phi is 1.618.