The power floors sequence for base 3/2 is 
,
where 
is the floor function. Its first few terms are
1, 1, 2, 3, 5, 7, 11, 17, 25, 38, ... (OEIS A002379).
The first few composite 
occur for 
, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, ...
(OEIS A046037), corresponding to the composites
25, 38, 57, 86, 129, 194, 291, 437, 656, ... (OEIS A070758).
Similarly, the first few prime 
occur for 
, 3, 4, 5, 6, 7, 21, 22, 98, ... (OEIS A070759),
corresponding to the primes 2, 3, 5, 7, 11, 17, 4987,
7481, 180693856682317883, ... (OEIS A067904).
The sequence 
is given by 1, 1, 1, 2, 3, 4, 5, 7,
9, 13, 17, 23, ... (OEIS A064628). The first
few composite 
occur for 
, 8, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, ... (OEIS A046038), corresponding to composites
4, 9, 42, 56, 74, 99, 133, 177, 236, ... (OEIS A070761).
Similarly, the first few prime 
occur for 
, 4, 6, 7, 9, 10, 11, 12, 38, 42, 59, 96, ... (OEIS A070762),
corresponding to the primes 2, 3, 5, 7, 13, 17, 23,
31, 55933, 176777, 23517191, 986549121979, ... (OEIS A067905).
There are infinitely many integers of the form 
and 
which are composite,
where 
is the floor function (Forman and Shapiro 1967;
Guy 1994, p. 220).
