%I #26 Sep 08 2022 08:46:07
%S 2,3,4,6,7,9,13,18,21,22,58,67,79,90,100,106,111,118,120,144,162,174,
%T 195,204,246,273,279,345,393,403,406,435,436,526,541,567,613,625,636,
%U 702,721,729,736,744,762,763,865,898,961,970,993,1059,1099,1117,1131
%N Numbers n such that (n-1)*n^2-1 and n^2-(n-1) are both prime.
%C Numbers n such that (n^3-n^2-1)*(n^2-n+1) is semiprime.
%C Intersection of A162293 and A055494.
%C Primes in this sequence: 2, 3, 7, 13, 67, 79, 541, 613, 1117, ...
%C Squares in this sequence: 4, 9, 100, 144, 961, ...
%H Giovanni Resta, <a href="/A239115/b239115.txt">Table of n, a(n) for n = 1..10000</a>
%e 13 is in this sequence because (13-1)*13^2-1 = 2027 and 13^2-(13-1) = 157 are both prime.
%t Select[Range[1000], PrimeQ[#^3 - #^2 - 1] && PrimeQ[#^2 - # + 1] &] (* _Giovanni Resta_, Mar 10 2014 *)
%t Select[Range[1200],PrimeOmega[#^5-2#^4+2#^3-2#^2+#-1]==2&] (* _Harvey P. Dale_, Sep 24 2014 *)
%o (PARI) isok(n) = isprime(n^3-n^2-1) && isprime(n^2-n+1); \\ _Michel Marcus_, Mar 10 2014
%o (Magma) k:=1;
%o for n in [1..1000] do
%o if IsPrime(k*(n-1)*n^2-1) and IsPrime(k*n^2-n+1) then
%o n;
%o end if;
%o end for; \\ _Juri-Stepan Gerasimov_, Mar 18 2014
%Y Cf. A162291, A002383, A239135, A239326.
%K nonn
%O 1,1
%A _Ilya Lopatin_ following a suggestion from _Juri-Stepan Gerasimov_, Mar 10 2014,
%E More terms from _Giovanni Resta_, Mar 10 2014