Values of k with 1 < k < prime(n)^2 such that prime(n) divides k^k + (-1)^k (k-1)^(k-1).
2, 19, 22, 9, 34, 8, 9, 47, 49, 62, 64, 102, 103, 118, 119, 9, 54, 103, 148, 165, 36, 59, 83, 101, 116, 124, 149, 157, 172, 190, 214, 237, 5, 35, 66, 106, 121, 128, 137, 206, 215, 222, 237, 277, 308, 338, 347, 3, 27, 75, 85, 126, 147, 169, 179, 209, 298, 328
3
It is odd that the period is prime(n)^2 instead of prime(n).
T. D. Noe, Plot of rows 3..50
T. D. Noe, Table of rows 3..50
(Mma) t7 = {}; Do[s = Select[Range[2, p^2], Mod[PowerMod[#, #, p] + (-1)^# PowerMod[# - 1, # - 1, p], p] == 0 &]; If[Length[s] > 0, AppendTo[t7, s]], {p, Prime[Range[50]]}]; t7
Cf. S000985.
nonn
T. D. Noe, Mar 21 2017