A127880 - OEIS

%I #14 Apr 30 2018 17:16:01

%S 43,55,103,115,223,307,319,379,403,487,505,607,643,715,757,763,775,

%T 799,883,925,979,1063,1069,1135,1147,1165,1189,1279,1309,1369,1543,

%U 1567,1585,1627,1693,1729,1783,1813,1819,1855,1903,1939,1945,2083,2149,2155

%N Numbers x for which x^4 + 4x^3 + 12x^2 + 24x + 24 is prime.

%C Generating polynomial is Schur's polynomial of 4-degree. Schur's polynomials n degree are n-th first term of series expansion of e^x function. All polynomials are non-reducible and belonging to the An alternating Galois transitive group if n is divisible by 4 or to Sn symmetric Galois Group in other case (proof Schur, 1930).

%H G. C. Greubel, <a href="/A127880/b127880.txt">Table of n, a(n) for n = 1..5000</a>

%p select(x->isprime(x^4+4*x^3+12*x^2+24*x+24),[$1..3000]); # _Muniru A Asiru_, Apr 30 2018

%t a = {}; Do[If[PrimeQ[24 + 24 x + 12 x^2 + 4 x^3 + x^4], AppendTo[a, x]], {x, 1, 1000}]; a

%o (PARI) isok(x) = isprime(x^4 + 4*x^3 + 12*x^2 + 24*x + 24); \\ _Michel Marcus_, Apr 30 2018

%o (GAP) Filtered([1..3000],x->IsPrime(x^4+4*x^3+12*x^2+24*x+24)); # _Muniru A Asiru_, Apr 30 2018

%Y Cf. A127873, A127874, A127875, A127876, A127877, A127878, A127879, A127881, A127882, A127883.

%K nonn

%O 1,1

%A _Artur Jasinski_, Feb 04 2007