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Look carefully at the numbers decreasing.. This should tell you that it is an "alternating" operation with an increasing parameter

f_n+1 = f_n ⊕_n+1 k_n+1

Alternating means that ⊕_n+1 depends on n+1. Especially on the modulus 2 group. And k_n+1 implies that the parameter depending of n+1. Especially it is its own "sequence".

Thank You.

First of all: I strongly disagree. It is a closed sequence. Not two interlaced ones.

Then: I'm absolutely against helping with concrete answers, Martin, cause these questions are basic math and IQ test related. You don't help the questionnaire at all.

Thus: An exception.

f_n+1 = f_n ⊕_n+1 k_n+1

0 |         = 2
1 |  2 +  1 = 3
2 |  3 - -1 = 4
3 |  4 +  2 = 6
4 |  6 -  0 = 6
5 |  6 +  3 = 9
6 |  9 -  1 = 8
7 |  8 +  4 = 12
8 | 12 -  2 = 10

Select allOpen in new window

⊕_n+1
The alternating operation is +-+-+-+-+-+-+-+- and so on.

⊕_n+1 := -|n+1 mod 2 = 0
⊕_n+1 := +|n+1 mod 2 = 1

and the parameter is

0 |               = 2    
1 |  2 +  (1 - 0) = 3
2 |  3 -  (1 - 2) = 4
3 |  4 +  (2 - 0) = 6
4 |  6 -  (2 - 2) = 6
5 |  6 +  (3 - 0) = 9
6 |  9 -  (3 - 2) = 8
7 |  8 +  (4 - 0) = 12
8 | 12 -  (4 - 2) = 10

Select allOpen in new window

k_n+1 := m_n+1   |n+1 mod 2 = 0
k_n+1 := m_n+1 - 2|n+1 mod 2 = 0

with

m₀ := 0
m_n+1 := m_n   |n+1 mod 2 = 0
m_n+1 := m_n + 1|n+1 mod 2 = 0

I think that both our answers are valid since 2 3 4 6 6 9 8 12 10 15 is interlaced. And about helping with "concrete answers" I understand your point but I believe EE decided some time ago that it's OK to help with homework type questions.