When ever a decay occurs the nucleon number either stays the same (gamma or beta emission) or reduces by four (alpha emission). Therefore if you divide the nucleon number by four you will either have no remainder or 1, 2 or 3. Mathematically we could say that the nucleon number could be described by 4n, 4n+1, 4n+2 or 4n+3.

One unstable nucleus will decay into another unstable nucleus, over and over in a "decay series" until an ultra-stable nucleus (usually a stable isotope of lead Pb ²⁰⁶, Pb ²⁰⁷ or Pb ²⁰⁸) is reached as the end product.

These are often represented graphically by plotting nucleon number against proton number.

a emissions become a diagonal line (proton number and nucleon number each decreasing by 2).

b emissions become a horizontal line (proton number increasing by one and nucleon number remaining the same)

g emissions cannot easily be represented when drawing these series but sometimes a wavy line is drawn in to accompany the a or b decay line.

Three such series occur naturally:

The Thorium Series (4n) - see below

The Actinium Series (4n+1)

The Uranium Series (4n+2) - see below

The 4n+3 series has only been possible since we made transuranic elements in nuclear reactions.