H2, Li, He, Be, N2, B, O2, C, F2, Na, Ne, Mg...

I took the "math sequence" path-I may be way out but - I'll give this a try:

first I put the elements next to its atomic number- Then I found what do I need to add or subtract (in atomic number units) to get the next element:for example H is 1, plus 2 gives Li; Li is 3, minus 1 gives He, and so on:

H2--1 (+2)

Li---3 (-1)

He--2 (+2)

Be--4 (+3)

N2--7 (-2)

B---5 (+3)

02--8 (-2)

C---6 (+3)

F2--9 (+2)

Na--11 (-1)

Ne--10 (+2)

Mg--12 (?)

Then I studied the sequence of signs:

(+ - +) ( + - +) (- + +) (- + ?) ( ? ? ?) ( ? ? ?) and I continued the sequence as follows:

(+ - +) ( + - +) (- + +) ( - + +) (+ - +) (+ - +).

Lastly the number sequence:

(2 1 2) (3 2 3) (2 3 2) (1 2 ?) ( ? ? ?) (? ? ?) I continued the sequence as:

(2 1 2) (3 2 3) (2 3 2 ) (1 2 1) (2 1 2) (3 2 3)

so putting all together: this will the completed sequence:

( +2 -1 +2) (+ 3 -2 +3) ( -2 +3 +2) (- 1+ 2+ 1) (+2 -1 +2) ( +3 -2 +3)

so completing the sequence on the top:

H2--1 (+2)

Li---3 (-1)

He--2 (+2)

Be--4 (+3)

N2--7 (-2)

B---5 (+3)

02--8 (-2)

C---6 (+3)

F2--9 (+2)

Na--11 (-1)

Ne--10 (+2)

Mg--12 (+1)

Al ---13 (+2)

P4----15 (-1)

Si---14 (+2)

S8----16

and I wrote them in standard states as all are on the list:so Al, P

_{4}, Si, S

_{8} is my answer