A104311 Numbers n such that the coefficient of x^n in (x^3+x^2+x+1)^n is prime.

2, 4, 5, 8, 73, 649

Offset

1,1

Comments

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.

Any further terms are > 500000. - Lucas A. Brown, Oct 04 2024

Links

Table of n, a(n) for n=1..6.

Mathematica

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}]

Crossrefs

Cf. A005725 (quadrinomial coefficients).

Sequence in context: A012973 A013154 A013129 * A200818 A021980 A303496

Adjacent sequences: A104308 A104309 A104310 * A104312 A104313 A104314

Keyword

more,nonn,hard

Author

T. D. Noe, Mar 01 2005

Status

approved