[seqfan] Smallest k>1 such that k^n+n is prime

[Hugo Pfoertner]

SeqFans,

usually I now refrain from inventing "is prime" sequences, but a friend
asked me, for which n there are no solutions for k^n+n=prime. The values of
n for which I could not find a matching k were n=4, 27, 64, next > 170. If
we say, k=0 if no such k exist, what are the next expected positions where
this happens?

A corresponding sequence from n=1 through n=65 would be:
2, 3, 2, 0, 2, 175, 16, 3, 2, 539, 32, 221, 118, 417, 2, 85, 14, 133, 22,
81, 76, 115, 12, 55, 28, 15, 0, 2465, 110, 31, 232, 117, 230, 3, 12, 851,
4, 375, 2, 1599, 48, 5461, 46, 15, 218, 6815, 78, 7, 100, 993, 28, 901,
624, 13, 252, 183, 226, 43247, 104, 5063, 1348, 777, 1294, 0, 1806,

Hugo Pfoertner