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A239326 Numbers k such that k^2 +/- (k-1) and (k-1)*k^2 +/- 1 are all primes.

%I A239326 #16 Sep 08 2022 08:46:07
%S A239326 2,3,6,13,21,100,120,195,393,541,1749,1849,3640,3829,4003,5488,5754,
%T A239326 8973,8989,9043,10824,10828,13488,17016,18493,19306,21505,24270,27139,
%U A239326 30163,31530,34134,35034,39514,40761,46215,46285,46398,49071,49869,53319,55320
%N A239326 Numbers k such that k^2 +/- (k-1) and (k-1)*k^2 +/- 1 are all primes.
%C A239326 Intersection of A239115 and A239135.
%H A239326 Daniel Starodubtsev, <a href="/A239326/b239326.txt">Table of n, a(n) for n = 1..10000</a>
%e A239326 6 is this sequence because (6-1)*6^2-1 = 179, (6-1)*6^2+1 = 181, 6^2-6+1 = 31 and 6^2+6-1 = 41 are all primes.
%o A239326 (Magma) k := 1;
%o A239326      for n in [1..100000] do
%o A239326         if IsPrime(k*(n - 1)*n^2 + 1) and IsPrime(k*(n - 1)*n^2 - 1) and IsPrime(k*n^2 + n - 1) and IsPrime(k*n^2 - n + 1) then
%o A239326            n;
%o A239326         end if;
%o A239326      end for;
%K A239326 nonn,easy
%O A239326 1,1
%A A239326 _Ilya Lopatin_ and _Juri-Stepan Gerasimov_, Mar 16 2014
%E A239326 Edited by _Alois P. Heinz_, Mar 19 2014