A104311 - OEIS

%I #8 Oct 04 2024 23:09:12

%S 2,4,5,8,73,649

%N Numbers n such that the coefficient of x^n in (x^3+x^2+x+1)^n is prime.

%C n such that A005725(n) is prime. No other n<16000. The primes are in A104312. Only coefficients of the x, x^n, x^(2n) and x^(3n-1) terms can be prime; the coefficients of x and x^(3n-1) terms are prime whenever n is prime.

%C Any further terms are > 500000. - _Lucas A. Brown_, Oct 04 2024

%t f=1; Do[f=Expand[f*(x^3+x^2+x+1)]; s=Coefficient[f, x, n]; If[PrimeQ[s], Print[{n, s}]], {n, 1000}]

%Y Cf. A005725 (quadrinomial coefficients).

%K more,nonn,hard

%O 1,1

%A _T. D. Noe_, Mar 01 2005