%I #8 Oct 16 2024 16:34:34
%S 2,5,11,23,47,19,3,7,29,59,17,103,619,2477,991,661,3967,2267,907,191,
%T 383,13,53,107,43,173,347,139,31,83,167,67,269,359,719,1439,2879,443,
%U 887,71,61,41,137,823,37,149,199,797,1063,709,2837,227,101,607,3643,21859
%N a(1) = 2. Let k >= 1 be the minimal integer such that 2*k*a(n-1) + 1 has at least one prime divisor which is not already in the sequence. Then a(n) is the smallest such divisor.
%C Conjectures: 1) The sequence is a permutation of prime numbers; 2) k = k(n) runs all positive integers.
%t a = {2}; Do[k = 1; While[(d = Complement[FactorInteger[2 k a[[-1]] + 1][[All, 1]], a]) == {}, k++]; AppendTo[a, Min@d], {n, 50}]; a (* _Jinyuan Wang_, Feb 26 2020 *)
%Y Cf. A005132, A063733, A078943, A174161.
%K nonn
%O 1,1
%A _Vladimir Shevelev_, Mar 10 2010
%E More terms from _Jinyuan Wang_, Feb 26 2020