A127880 Numbers x for which x^4 + 4x^3 + 12x^2 + 24x + 24 is prime.

43, 55, 103, 115, 223, 307, 319, 379, 403, 487, 505, 607, 643, 715, 757, 763, 775, 799, 883, 925, 979, 1063, 1069, 1135, 1147, 1165, 1189, 1279, 1309, 1369, 1543, 1567, 1585, 1627, 1693, 1729, 1783, 1813, 1819, 1855, 1903, 1939, 1945, 2083, 2149, 2155

Offset: 1

Author

Artur Jasinski, Feb 04 2007

Keywords

• nonn

Comments

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).

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

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

Programs

GAP

Filtered([1..3000],x->IsPrime(x^4+4*x^3+12*x^2+24*x+24)); # Muniru A Asiru, Apr 30 2018

Maple

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

Mathematica

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

PARI

isok(x) = isprime(x^4 + 4*x^3 + 12*x^2 + 24*x + 24); \\ Michel Marcus, Apr 30 2018