import numpy as np
import matplotlib.pyplot as plt
from matplotlib.ticker import AutoMinorLocator

def forw(x):
    return x/5.2

def rev(x):
    return x*5.2

p_xax = [i for i in range(0,21,5)]
p_yax = [i for i in range(0,13,3)]
plt.scatter(p_xax, p_yax, color='black')
plt.xlabel("Main xaxis")
plt.ylabel("Main yaxis")
plt.xlim(0,20)
plt.ylim(0,15)
plt.xticks(np.arange(0,21,5))
plt.yticks(np.arange(0,16,3))

ax = plt.gca()
ax.xaxis.set_minor_locator(AutoMinorLocator(2))
ax.yaxis.set_minor_locator(AutoMinorLocator(2))

sec = ax.secondary_xaxis('top', functions=(forw, rev))
sec.set_xlabel(r"Secondary xaxis")
sec.set_ticks(np.arange(0,3.5,1), minor=True)
plt.savefig("test_plot.png")