We consider a directed abelian sandpile on a strip of size 2×n,
driven by adding a grain randomly at the left boundary after every T
time-steps. We establish the exact equivalence of the problem of mass
fluctuations in the steady state and the number of zeroes in the ternary-base
representation of the position of a random walker on a ring of size 3n. We
find that while the fluctuations of mass have a power spectrum that varies as
1/f for frequencies in the range 3−2n≪f≪1/T, the activity
fluctuations in the same frequency range have a power spectrum that is linear
in f.Comment: 8 pages, 10 figure