As part of the NASA Kepler Guest Observer program, we requested and obtained long-cadence data on about 2700 faint (magnitude 14-16) Kepler stars with effective temperatures and surface gravities that lie near or within the pulsation instability region for main-sequence gamma Doradus and delta Scuti pulsating variables. These variables are of spectral type A-F with masses of 1.4 to 2.5 solar masses. The delta Scuti stars pulsate in radial and non-radial acoustic modes, with periods of a few hours (frequencies around 10 cycles/day), while gamma Doradus variables pulsate in nonradial gravity modes with periods 0.3 to 3 days (frequencies around 1 cycle/day). Here we consider the light curves and Fourier transforms of 633 stars in an unbiased sample observed by Kepler in Quarters 6-13 (June 2010-June 2012). We show the location of these stars in the log surface gravity--effective temperature diagram compared to the instability region limits established from ground-based observations, and taking into account uncertainties and biases in the Kepler Input Catalog T_eff values. While hundreds of variables have been discovered in the Kepler data, about 60% of the stars in our sample do not show any frequencies between 0.2 and 24.4 cycles per day with amplitude above 20 parts per million. We find that six of these apparently constant stars lie within the pulsation instability region. We discuss some possible reasons that these stars do not show photometric variability in the Kepler data. We also comment on the non-constant stars, and on 26 variable-star candidates, many of which also do not lie within the expected instability regions.
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