One reasonable and memorable approximation excluding any fine structure is:
Equation 1. Hydrogen spectral series mnemonic
see for example example: hydrogen 1-2 spectral line.
Equation "Hydrogen spectral series mnemonic" gives for example from principal quantum number 1 to 2 a difference:
which with Planck-Einstein relation gives about 121.6 nm ( Hz), which is a reasonable match with the value of 121.567... from the NIST Atomic Spectra Database.

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