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A109904 a(1) = 5. a(n+1) is the greatest prime of the form k*(a(n)-k) + 1. The least prime occurs for k = 1 and a(n+1) = a(n) in that case if no other value of k gives a prime then the sequence terminates.

%I A109904 #14 Aug 02 2021 15:02:18
%S A109904 5,7,13,43,463,53593,718052371,128899801874680399,
%T A109904 4153789730832965126116749598699801,
%U A109904 4313492281993349218329412357362100514520987205269104143837429352069
%N A109904 a(1) = 5. a(n+1) is the greatest prime of the form k*(a(n)-k) + 1. The least prime occurs for k = 1 and a(n+1) = a(n) in that case if no other value of k gives a prime then the sequence terminates.
%C A109904 For the first five terms k = floor(a(n)/2). k can take values from 1 to floor(a(n)/2). It is conjectured that at least one value of k, 2 <= k < floor(a(n)/2) gives a prime and the sequence is infinite.
%H A109904 Jinyuan Wang, <a href="/A109904/b109904.txt">Table of n, a(n) for n = 1..13</a>
%e A109904 a(2) = 2*3 + 1 = 7, a(3) = 3*4 + 1 = 13.
%o A109904 (PARI) { b(n)=forstep(k=n\2,1,-1,if(isprime(k*(n-k)+1),return(k*(n-k)+1)));return(0) }
%o A109904 s=5;while(1,print1(s, ", ");s=b(s)) \\ _Max Alekseyev_, Oct 04 2005
%Y A109904 Cf. A026728, A109905.
%K A109904 nonn
%O A109904 1,1
%A A109904 _Amarnath Murthy_, Jul 15 2005
%E A109904 More terms from _Max Alekseyev_, Oct 04 2005