  A search for the decays of the $B_c^+$ meson to $p\bar p\pi^+$ is performed
for the first time using a data sample corresponding to an integrated
luminosity of 3.0 $\mathrm{fb}^{-1}$ collected by the LHCb experiment in $pp$
collisions at centre-of-mass energies of $7$ and $8$ TeV. No signal is found
and an upper limit, at 95\% confidence level, is set,
$\frac{f_c}{f_u}\times\mathcal{B}(B_c^+\to p\bar p\pi^+)<3.6\times10^{-8}$ in
the kinematic region $m(p\bar p)<2.85\mathrm{\,Ge\kern -0.1em V\!/}c^2$,
$p_{\rm T}(B)<20\mathrm{\,Ge\kern -0.1em V\!/}c$ and $2.0<y(B)<4.5$, where
$\mathcal{B}$ is the branching fraction and $f_c$ ($f_u$) is the fragmentation
fraction of the $b$ quark into a $B_c^+$ ($B^+$) meson.
