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%I #7 Sep 11 2021 06:58:35
%S 1,459,3,252,16,104,246,562,895,459,3656,165,409,869,3075,1568,1310,
%T 7723,4035,21114,10634,2185,143,11861,24850,3168,4750,14373,565,22576,
%U 7971,2063,17528,58449,13461,2988,45498,51682,13498,22185,16174,49145,940,86418,66380
%N a(n) is the least k such that (k*prime(n)#)^2 + 1, ((k+1)*prime(n)#)^2 + 1 and ((k+2)*prime(n)#)^2 + 1 are 3 primes, where prime(n)# is the n-th primorial.
%e (3*2*3*5)^2+1 = 8101 is prime, (4*2*3*5)^2+1 = 14401 is prime, and (5*2*3*5)^2+1 = 22501 is prime, so a(3) = 3.
%t a[n_] := Module[{k = 1, p = Product[Prime[i], {i, 1, n}]}, While[!PrimeQ[(k*p)^2 + 1] || !PrimeQ[((k + 1)*p)^2 + 1] || !PrimeQ[((k + 2)*p)^2 + 1], k++]; k]; Array[a, 10] (* _Amiram Eldar_, Sep 11 2021 *)
%Y Cf. A002110.
%K nonn
%O 1,2
%A _Pierre CAMI_, Oct 02 2004
%E a(2) corrected and more terms added by _Amiram Eldar_, Sep 11 2021
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