Fun with Science

Although the number of neutrons in an atom can be calculated using the formula
Number of neutrons=Atomic mass - Number of Protons
Upon closer examination, I have come to find a trend in the numbers.However, I have limited it to Calcium as the numbers get more complicated as the atomic number increases.The trend, in layman's terms, is just an arithmetic progression.

If the atomic number is subtracted from the number of neutrons for the first twenty elements, an interesting trend shows up.
Starting from Hydrogen and proceeding towards Calcium:
-1, 0, {1, 1, 1, 0, 0, 0}, 1, 0, 1, 0, 1, 0, 1, 0, 1,{4}, 1, 0
The only exceptions in the pattern are Hydrogen and Argon; Hydrogen has no neutrons at all and Argon has 4 more neutrons than protons (i.e. Atomic Number).
Sub-trend 1:
In the pattern mentioned above, I have placed "1 , 1 , 1 , 0 , 0 , 0" in { } because blatantly, they form an interesting pattern. A triplet of "1" and a triplet of "0".
Sub-trend 2:
From Fluorine to Chlorine, a spellbinding pattern forms. A boolean of 1s and 0s.A "one" followed by a "zero". At Argon, the pattern is being "interrupted"; however, if we do consider the "4" in Argon to be "0", the pattern continues undisturbed for the next two elements also.
Drawback:
This pattern, however, only follows till Calcium. After calcium, the numbers go astray.
3 , 4 , 5 , 4 , 5 , 4 , 4 , 2 , 6 , 5
Although I have observed this, as of now, I cannot think of an explanation nor have I found it anywhere on the Internet or past scientific journals.Nevertheless, I continue to search for an explanation.

Author Introduction
Adithya from grade 9A is very passionate about science and math and engrossed in scientific theory and analysis, made by various scientists. He also loves to present his own theories and conclusions in this field.