Curious Proth Primes

This is an ad hoc collection of interesting facts about "Proth primes" of the form k*2^n+1, or of such Proth primes which are curious in some way -- generally by being rare or by holding some sort of record...
First, some definitions:

KSEQ(n)[1] == KSEQ(n+1)[1]

For these values of n, we have the curious coincidence that KSEQ(n)[1] == KSEQ(n+1)[1]:

KSEQ(n)[1]/n >= 5

For these values of n, we have a curious drought of primes for "small" k: Note that for 1 <= n <= 6085, the mean value of KSEQ(n)[1]/n is equal to 0.717, so a ratio of 5 is approximately 7 times larger than the average.