  Aims. We introduce the TELAMON program which is using the Effelsberg 100-m
telescope to monitor the radio spectra of active galactic nuclei (AGN) under
scrutiny in astroparticle physics, specifically TeV blazars and candidate
neutrino-associated AGN. Here, we present and characterize our main sample of
TeV-detected blazars.
  Methods. We analyze the data sample from the first ~2.5 years of observations
between August 2020 and February 2023 in the range from 14 GHz to 45 GHz.
During this pilot phase, we have observed all 59 TeV-detected blazars in the
Northern Hemisphere (i.e., Dec. >0{\deg}) known at the time of observation. We
discuss the basic data reduction and calibration procedures used for all
TELAMON data and introduce a sub-band averaging method used to calculate
average light curves for the sources in our sample.
  Results. The TeV-selected sources in our sample exhibit a median flux density
of 0.12 Jy at 20 mm, 0.20 Jy at 14 mm and 0.60 Jy at 7 mm. The spectrum for
most of the sources is consistent with a flat radio spectrum and we find a
median spectral index ($S(\nu)\propto\nu^\alpha$) of $\alpha=-0.11$. Our
results on flux density and spectral index are consistent with previous studies
of TeV-selected blazars. Compared to the GeV-selected F-GAMMA sample, TELAMON
sources are significantly fainter in the radio band. This is consistent with
the double-humped spectrum of blazars being shifted towards higher frequencies
for TeV-emitters (in particular for high-synchrotron peaked BL Lac type
objects), which results in a lower radio flux density. The spectral index
distribution of our TeV-selected blazar sample is not significantly different
from the GeV-selected F-GAMMA sample. Moreover, we present a strategy to track
the light curve evolution of sources in our sample for future variability and
correlation analysis.
