The isodiapher concept provides a means of organizing stable nuclei.
In this corner...
An atomic nucleus with more than one nucleon (if it is smaller than a neutron star) essentially represents a battle between two forces through which the nucleons interact:
electrostatic forces, which tend to favor more neutrons for a given mass number due to repulsion between like charges
internuclear forces, which are more attractive between a proton and a neutron than between like nucleons and thus tend to favor equal numbers of neutrons and protons.
The neutron-proton difference thus represents a measure of the extent to which electrostatic forces intervene and prevent an atomic nucleus from reaching equal numbers of protons and neutrons. Isodiaphers therefore represent a similar balance between these forces and thus have similar stability characteristics, at least if the atomic masses are close enough.
Perhaps the most prominent example of this similarity involves one family of isodiaphers, having a difference of zero. These are atoms where electrostatic forces are small enough to allow the internuclear forces their way with proton-neutron balance. Included in this series are the only four odd-odd nuclei that are fully stable against radioactive decay: deuterium, lithium-6, boron-10 and nitrogen-14. In other words, odd-odd nuclei are stabilized by the specific combination of maximal internuclear attraction with small electrostatic repulsion.
Beyond nitrogen-14, this zero-difference family becomes more like other isodiapheric families. Because the electrostatic/internuclear force balance shifts only slowly with increasing mass number, we see the fully stable nuclei arranged into parallel, overlapping families having a common nucleon difference. With an even difference we see the isodiaphers at every other element, like neon-20, magnesium-24 and silicon-28 in the zero-difference series; and titanium-48, chromium-52 and iron-56 in the +4 series. This occurs because of the stability difference between even-even and odd-odd nuclei heavier than nitrogen-14. When the nucleon difference is odd, this parity effect is absent and then we can see isodiaphers at adjacent elements, like neon-21, sodium-23, magnesium-25, aluminum-27 and silicon-29 (+1) -- which includes all five of those elements versus only three of the five for the heavier part of the zero-difference family given earlier.