
COMMENTS

A prime p is a kWallSunSun prime iff p^2 divides F_k(pi_k(p)), where F_k(n) is the kFibonacci numbers, i.e., a Lucas sequence of first kind with (P,Q) = (k,1), and pi_k(p) is the Pisano period of kFibonacci numbers modulo p (cf. A001175, A175181A175185).
For prime p > 2 not dividing k^2 + 4, it is a kWallSunSun prime iff p^2  F_k(p((k^2+4)/p)), where ((k^2+4)/p) is the Kronecker symbol.
a(1) would be the smallest WallSunSun prime whose existence is an open question.
a(12)..a(16) = 2, 3, 3, 29, 2. a(18)..a(33) = 3, 11, 2, 23, 3, 3, 2, 5, 79, 3, 2, 7, 23, 3, 2, 239. a(36)..a(38) = 2, 7, 17. a(40), a(41) = 2, 3. a(43)..a(46) = 5, 2, 3, 41.  R. J. Mathar, Apr 22 2016
a(17) = 1192625911, a(35) = 153794959, a(39) = 30132289567, a(47)..a(50) = 139703, 2, 3, 3. If they exist, a(11), a(34), a(42) are greater than 10^12.  Max Alekseyev, Apr 26 2016
Column k = 1 of table T(n, k) of kth nWallSunSun prime (that table is not yet in the OEIS as a sequence).  Felix Fröhlich, Apr 25 2016
From Richard N. Smith, Jul 16 2019: (Start)
a(n) = 2 if and only if n is divisible by 4.
a(n) = 3 if and only if n == 5, 9, 13, 14, 18, 22, 23, 27, 31 (mod 36). (End)
