

A241975


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


1



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
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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^2n1), 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



