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We study Piatetski‐Shapiro sequences(   ⌊   n  c   ⌋   )   n    modulo   m  , for non‐integer    c  >  1    and positive   m  , and we are particularly interested in subword occurrences in those sequences. We prove that each block    ∈    {  0  ,  1  }   kof length    k  <  c  +  1    occurs as a subword with the frequency    2   −  k    , while there are always blocks that do not occur. In particular, those sequences are not normal. For    1  <  c  <  2   , we estimate the number of subwords from above and below, yielding the fact that our sequences are deterministic and not morphic. Finally, using the Daboussi–Kátai criterion, we prove that the sequence    ⌊   n  c   ⌋    modulo   m   is asymptotically orthogonal to multiplicative functions bounded by 1 and with mean value 0.

RANDOMNESS AND NON‐RANDOMNESS PROPERTIES OF PIATETSKI‐SHAPIRO SEQUENCES MODULO m