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A182424 Numbers n such that n^4 + n^3 + n^2 + n - 1 is prime.

%I A182424 #17 Sep 08 2022 08:45:55
%S A182424 1,2,6,8,11,12,18,30,32,39,41,44,50,63,65,69,72,74,75,78,86,93,104,
%T A182424 107,110,123,126,140,149,153,158,165,177,179,182,186,188,189,215,218,
%U A182424 222,225,236,237,239,254,264,267,272,278,296,299,302,305,314,320,327,330
%N A182424 Numbers n such that n^4 + n^3 + n^2 + n - 1 is prime.
%C A182424 The sequence contains 60491 terms <= 10^6.
%C A182424 The corresponding sequence of primes begins 3, 29, 1553, 4679, 16103, 22619, 111149, 837929, 1082399, 2374319, 2896403, 3835259, 6377549, 16007039, ...
%H A182424 Vincenzo Librandi, <a href="/A182424/b182424.txt">Table of n, a(n) for n = 1..7000</a>
%e A182424 18^4 + 18^3 + 18^2 + 18 - 1 = 111149 is prime, so 18 is in the sequence.
%t A182424 Select[Range[350],PrimeQ[Total[#^Range[4]]-1]&] (* _Harvey P. Dale_, Aug 09 2014 *)
%o A182424 (PARI)
%o A182424 for (n=1,10^4, p=n^4 + n^3 + n^2 + n - 1; if (isprime(p), print1(n,", ")));
%o A182424 /* _Joerg Arndt_, Apr 28 2012 */
%o A182424 (Magma) [n: n in [0..400] | IsPrime(s) where s is -1+&+[n^i: i in [1..4 by 1]]]; // _Vincenzo Librandi_, Aug 10 2014
%Y A182424 Cf. A049409, A182385.
%K A182424 nonn
%O A182424 1,2
%A A182424 _Alex Ratushnyak_, Apr 28 2012