A098765 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.

1, 459, 3, 252, 16, 104, 246, 562, 895, 459, 3656, 165, 409, 869, 3075, 1568, 1310, 7723, 4035, 21114, 10634, 2185, 143, 11861, 24850, 3168, 4750, 14373, 565, 22576, 7971, 2063, 17528, 58449, 13461, 2988, 45498, 51682, 13498, 22185, 16174, 49145, 940, 86418, 66380

Offset

1,2

Links

Table of n, a(n) for n=1..45.

Example

(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.

Mathematica

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 *)

Crossrefs

Cf. A002110.

Sequence in context: A252408 A251474 A251468 * A286845 A062043 A331468

Adjacent sequences: A098762 A098763 A098764 * A098766 A098767 A098768

Keyword

nonn

Author

Pierre CAMI, Oct 02 2004

Extensions

a(2) corrected and more terms added by Amiram Eldar, Sep 11 2021

Status

approved