%I A104313
%S A104313 2,3,28,30,31
%N A104313 Numbers n such that the coefficient of x^(2n) in (x^4+x^3+x^2+x+1)^n 
               is prime.
%C A104313 n such that A005191(n) is prime. No other n<10000. The primes are in 
               A104314. Only coefficients of the x, x^(2n) and x^(4n-1) terms can 
               be prime; the coefficients of x and x^(4n-1) terms are prime whenever 
               n is prime.
%C A104313 No other n<195316. Most likely this sequence is finite. Terms A005191(n) 
               that are not a multiple of 5 have zero density, namely, there are 
               fewer than n^(log(4)/log(5)) such terms among A005191(1..n). In particular, 
               A005191(5k+2) and A005191(5k+4) are multiples of 5 for every k. - 
               Max Alekseyev (maxale(AT)gmail.com), Apr 25 2005
%t A104313 f=1; Do[f=Expand[f*(x^4+x^3+x^2+x+1)]; s=Coefficient[f, x, 2n]; If[PrimeQ[s], 
               Print[{n, s}]], {n, 100}]
%Y A104313 Cf. A005191 (pentanomial coefficients).
%Y A104313 Sequence in context: A010344 A037316 A032813 this_sequence A037423 A009249 
               A012697
%Y A104313 Adjacent sequences: A104310 A104311 A104312 this_sequence A104314 A104315 
               A104316
%K A104313 more,nonn
%O A104313 1,1
%A A104313 T. D. Noe (noe(AT)sspectra.com), Mar 01 2005