A241975 Numbers n such that n^4 - n^3 - n - 1 is a semiprime.

4, 6, 10, 14, 16, 20, 36, 40, 54, 56, 66, 84, 90, 94, 116, 126, 146, 150, 156, 160, 170, 204, 210, 260, 264, 306, 340, 350, 386, 396, 406, 420, 464, 474, 496, 570, 634, 674, 696, 700, 716, 740, 764, 780, 816, 826, 864, 890, 966, 1054, 1070, 1094, 1106, 1144

Offset

1,1

Comments

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]

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..400

Mathematica

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

Prog

(Magma) IsSemiprime:=func<n | &+[ k[2]: k in Factorization(n) ] eq 2 >; [ n: n in [2..1500] | IsSemiprime(n^4 - n^3 - n - 1)];
(PARI) for(n=1, 10^4, if(isprime(n^2+1)&&isprime(n^2-n-1), print1(n, ", "))) \\ Derek Orr, Aug 10 2014

Crossrefs

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

Sequence in context: A171945 A310583 A298784 * A063745 A123666 A095305

Adjacent sequences: A241972 A241973 A241974 * A241976 A241977 A241978

Keyword

nonn,less

Author

Vincenzo Librandi, Aug 10 2014

Status

approved