How do I find the closest values in a Pandas series to an input number?

You could use argsort() like

Say, input = 3

In [198]: input = 3

In [199]: df.iloc[(df['num']-input).abs().argsort()[:2]]
Out[199]:
   num
2    4
4    2

df_sort is the dataframe with 2 closest values.

In [200]: df_sort = df.iloc[(df['num']-input).abs().argsort()[:2]]

For index,

In [201]: df_sort.index.tolist()
Out[201]: [2, 4]

For values,

In [202]: df_sort['num'].tolist()
Out[202]: [4, 2]

Detail, for the above solution df was

In [197]: df
Out[197]:
   num
0    1
1    6
2    4
3    5
4    2