
COMMENTS

After a(22) = 95423329, no more terms through 10^8.
The corresponding (p,n): (341,3), (645,2), (645,3), (341,11), (645,5), (561,8), (1729,2), (1387,5), (341,120), (561,44), (1905,5), (645,47), (3277,2), (2701,3), (2047,9), (4369,2), (341,384), (2821,6), (2047,13), (2465,12), (3277,7), (4369,5).
Conjecture: For any Fermat pseudoprime p to base 2 there are infinitely many Fermat pseudoprimes to base 2 equal to p^2*n  p*n + p, where n is a positive integer.
See the sequence A215343: the generalized formula from there is p^2*n  p*n + p^2, which suggests an extrapolated formula for obtaining some Fermat pseudoprime to base 2 from another: p^2*n  p*n + p^k.
Conjecture: For any Fermat pseudoprime p to base 2 and any positive integer k, there are infinitely many Fermat pseudoprimes to base 2 equal to p^2*n  p*n + p^k, where n is a positive integer.
