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%I #10 Aug 28 2021 06:42:45
%S 1,1,1,1,13,1,101,130,109,418,388,876,5011,11529
%N a(1) is the least k such that p(1) = (k*3)^2 + k*3 - 1 is prime, then a(n+1) is the least k such that (k*p(n))^2 + k*p(n) - 1 = p(n+1) is prime.
%C The p(n) sequence starts 11, 131, 17291, 298995971, 15108361827832297751, ...
%e a(1) = 1 as 3^2 + 3 - 1 = 11 = p(1) is prime.
%t f[0] = {0, 3}; f[n_] := f[n] = Module[{k = 1, p = f[n - 1][[2]]}, While[! PrimeQ[(k*p)^2 + k*p - 1], k++]; {k, (k*p)^2 + k*p - 1}]; Table[f[n][[1]], {n, 1, 10}] (* _Amiram Eldar_, Aug 28 2021 *)
%Y Cf. A120393, A120394, A120395, A120396.
%K nonn
%O 1,5
%A _Pierre CAMI_, Jul 01 2006
%E a(11)-a(14) from _Amiram Eldar_, Aug 28 2021
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