Quote:
Originally Posted by enzocreti
Is it possible to find such k up to 10^6?

It is! I find 678 such members. You could, too, with my code below and a copy of
PARI/GP. The parameters are pretty extensible in case you'd like to modify things.
Code:
liste(lim,mul,base=34,step=5590,offset=588)=my(v=List(),X=mul*base); lim\=1; while(X<lim,forstep(n=X+offset+step,lim,step, listput(v,n)); X*=base); Set(v)
list(lim)=setunion(liste(lim,23),liste(lim,223))
v=list(1e6)
Up to a billion I find 1370532 or 0.1%. Asymptotically I think the density is about 1.5% (42/2795) but it will take a while to get there.