A241975 - OEIS

%I #23 Sep 08 2022 08:46:07

%S 4,6,10,14,16,20,36,40,54,56,66,84,90,94,116,126,146,150,156,160,170,

%T 204,210,260,264,306,340,350,386,396,406,420,464,474,496,570,634,674,

%U 696,700,716,740,764,780,816,826,864,890,966,1054,1070,1094,1106,1144

%N Numbers n such that n^4 - n^3 - n - 1 is a semiprime.

%C Since n^4 - n^3 - n - 1 = (n^2 + 1)*(n^2 - n - 1), these are also numbers n such that n^2 + 1 and n^2 - n - 1 are both prime. Numbers in the intersection of A005574 and A002328. - _Derek Orr_, Aug 10 2014 [Sequence numbers corrected by _Jens Kruse Andersen_, Aug 11 2014]

%H Vincenzo Librandi, <a href="/A241975/b241975.txt">Table of n, a(n) for n = 1..400</a>

%t Select[Range[2000], PrimeOmega[#^4 - #^3 - # - 1]==2 &]

%o (Magma) IsSemiprime:=func<n | &+[ k[2]: k in Factorization(n) ] eq 2 >; [ n: n in [2..1500] | IsSemiprime(n^4 - n^3 - n - 1)];

%o (PARI) for(n=1,10^4,if(isprime(n^2+1)&&isprime(n^2-n-1),print1(n,", "))) \\ _Derek Orr_, Aug 10 2014

%Y Cf. A001358, A002327, A002496, A085722, A241670, A243436.

%K nonn,less

%O 1,1

%A _Vincenzo Librandi_, Aug 10 2014