A127882 - OEIS

%I #12 May 01 2018 21:31:03

%S 163,977611,12294697,37985853397,49252877161,137434331779,

%T 830329719061,1626105882361,8060524420261,11467771684597,

%U 13008402510163,15315610041211,43633838254429,71635442712061,125119099806661

%N Primes of the form 60*(x^5/120 + x^4/24 + x^3/6 + x^2/2 + x + 1).

%C Generating polynomial is Schur's polynomial of 5-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="/A127882/b127882.txt">Table of n, a(n) for n = 1..5000</a>

%p select(isprime,[seq(60*(x^5/120+x^4/24+x^3/6+x^2/2+x+1),x=1..2000)]); # _Muniru A Asiru_, Apr 30 2018

%t a = {}; Do[If[PrimeQ[60 + 60*x + 30*x^2 + 10*x^3 + (5*x^4)/2 + x^5/2], AppendTo[a, 60 + 60*x + 30*x^2 + 10*x^3 + (5*x^4)/2 + x^5/2]], {x, 1, 1000}]; a

%o (GAP) Filtered(List([1..2000],x->60*(x^5/120+x^4/24+x^3/6+x^2/2+x+1)),IsPrime); # _Muniru A Asiru_, Apr 30 2018

%Y Cf. A127873, A127874, A127875, A127876, A127877, A127878, A127879, A127880, A127881, A127883.

%K nonn

%O 1,1

%A _Artur Jasinski_, Feb 04 2007