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%I #8 Apr 10 2021 22:43:36
%S 3,3,3,205,2326161,20589460461,3847314721101
%N a(n) is the smallest number b such that (b^(2^k) + 1)/2 is prime for k = 0, 1, ..., n.
%e For n=3, the four numbers (205+1)/2, (205^2+1)/2, (205^4+1)/2, and (205^8+1)/2 are prime, and 205 is smallest with this property, so a(3)=205.
%o (PARI) a(n)=forstep(b=3,+oo,2,for(k=0,n,!ispseudoprime((b^(2^k)+1)/2)&&next(2));return(b)) \\ if a(n-1) is known, b loop can start from there instead
%Y Cf. A090872, A275530.
%K nonn,more,hard
%O 0,1
%A _Jeppe Stig Nielsen_, Apr 05 2021
%E a(6) found by _Kellen Shenton_ added by _Jeppe Stig Nielsen_, Apr 09 2021