[seqfan] ^2 + 2^

[2stepan at rambler.ru]

Dear SeqFans:
1) 2, 3, 3, 3, 5, 3, 3, 3, 5, 3, 3, .smallest prime p such that p^2 + 2^ n is
prime;
2) 5, 11, 13, 17, 41, 41, 73, 137, 281, 521, 1033, ..smallest prime of the form
p^2 + 2^n for some prime p;
3) 0, 1, 2, 2, 4, 2, 2, 8, 6, 4, 4, 2, 4, 6, 2, 10, 12, 12, 2, 8, 2, 4, 26, 4, 2,
8, 2, 10, 4, 14, 6, 8, 2, 4, 2, 4, 10, 2, 2, 206, ...
smallest k such that prime(n)^2 + 2^k is prime;
4) -1, 0, 1, 1, 2, 1, 1, 3, -1, 2, 2, 1, 2, -1, 1, -1, -1, 4, 1, 3, 1, 2, -1, 2,
1, 3, 1, ...
smallest k such that prime(n)^2 + 2^(2^k)) is prime, or -1 if no such k exists.
This [ 1), 2), 3) and 4) ] sequence is of general interest? Best, JSG