  We quantify the fraction of galaxies at moderate redshifts (0.1<z<0.5) that
appear red-and-dead in the optical, but in fact contain obscured star formation
detectable in the infrared (IR), with the PRIsm MUlti-object Survey (PRIMUS).
PRIMUS has measured ~120,000 robust redshifts with a precision of
sigma_z/(1+z)~0.5% over 9.1 square degrees of the sky to the depth of i~23
(AB), up to redshift z~1. We specifically targeted 6.7 square degree fields
with existing deep IR imaging from the Spitzer Space Telescope from the SWIRE
and S-COSMOS surveys. We select in these fields an i band flux-limited sample
(i<20 mag in the SWIRE fields and i<21 mag in the S-COSMOS field) of 3310
red-sequence galaxies at 0.1<z<0.5 for which we can reliably classify obscured
star-forming and quiescent galaxies using IR color. Our sample constitutes the
largest galaxy sample at intermediate redshift to study obscured star formation
on the red sequence, and we present the first quantitative analysis of the
fraction of obscured star-forming galaxies as a function of luminosity. We find
that on average, at L ~ L*, about 15% of red-sequence galaxies have IR colors
consistent with star-forming galaxies. The percentage of obscured star-forming
galaxies increases by ~8% per mag with decreasing luminosity from the highest
luminosities to L~0.2L*. Our results suggest that a significant fraction of
red-sequence galaxies have ongoing star formation and that galaxy evolution
studies based on optical color therefore need to account for this complication.
