# Can this sequence be expressed with a formula?

Can this sequence be expressed with a formula?

1 1 1

2 2

3 3 3

4 4 4

5 5

6 6 6

7 7

8 8 8

9 9 9

10 10

11 11 11

12 12 12

13 13

14 14 14

15 15

16 16 16

17 17 17

18 18

19 19 19

20 20

21 21 21

22 22 22

23 23

24 24 24

25 25 25

26 26

27 27 27

28 28

29 29 29

30 30 30

31 31

32 32 32

33 33 33

34 34

35 35 35

36 36

37 37 37

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I don't know if such a formula exists, but à priori this one is good at evaluating the terms up to $\sim 30$ where it starts to fail: $$\left\lfloor\dfrac{n}{1+\phi}\right\rfloor=\left\lfloor\dfrac{n}{\phi^2}\right\rfloor\quad n\in\Bbb N$$ where $\phi$ is the golden ratio.
@popovitsj My first answer didn't work, that's why I replaced it with this new one. (How did it work for you?) It is not an equation, it's just because you can express it in two different ways since $1+\phi=\phi^2$, where $\phi=\dfrac{1+\sqrt5}2$. –  Hakim Apr 20 at 11:03