cp's OEIS Frontend

A241670 Semiprimes of the form n^4 - n^3 - n - 1.

%I A241670 #21 Sep 08 2022 08:46:07
%S A241670 187,1073,8989,35657,61423,151979,1632923,2495959,8345537,9658823,
%T A241670 18687173,49194347,64880909,77244217,179502923,250046873,451259573,
%U A241670 502874849,588444323,651263839,830296829,1723401587,1935548789,4552183739,4839132407,8739047573,13324055659
%N A241670 Semiprimes of the form n^4 - n^3 - n - 1.
%C A241670 Since n^4 - n^3 - n - 1 = (n^2 + 1)*(n^2 - n - 1), it is a must that (n^2 + 1) and (n^2 - n - 1) both should be prime.
%C A241670 Primes of the form (n^2+1) are at A002496.
%C A241670 Primes of the form (n^2-n-1) are at A002327.
%H A241670 K. D. Bajpai, <a href="/A241670/b241670.txt">Table of n, a(n) for n = 1..5330</a>
%e A241670 187 is in the sequence because 4^4 - 4^3 - 4 - 1 = 187 = 11 * 17, which is semiprime.
%e A241670 1073 is in the sequence because 6^4 - 6^3 - 6 - 1 = 1073 = 29 * 37, which is semiprime.
%p A241670 select(k -> numtheory:-bigomega(k)=2, [seq(x^4 - x^3 - x - 1, x=1..1000)]);
%t A241670 Select[Table[n^4 - n^3 - n - 1, {n, 500}], PrimeOmega[#] == 2 &]
%o A241670 (PARI)
%o A241670 for(n=1,10^4,p=n^2+1;q=n^2-n-1;if(isprime(p)&&isprime(q),print1(p*q,", "))) \\ _Derek Orr_, Aug 09 2014
%o A241670 (Magma) IsSemiprime:= func<n | &+[d[2]: d in Factorization(n)] eq 2>; [s: n in [1..400] | IsSemiprime(s) where s is n^4 - n^3 - n - 1]; // _Vincenzo Librandi_, Aug 10 2014
%Y A241670 Cf. A000040, A001358, A002327, A002496.
%K A241670 nonn,less
%O A241670 1,1
%A A241670 _K. D. Bajpai_, Aug 09 2014