A104314 -id:A104314 - cp's OEIS frontend

A104312 Prime coefficient of x^n in (x^3+x^2+x+1)^n for n in A104311.

3, 31, 101, 3823, 2266366724843687556556015073508073201681

Offset: 1

T. D. Noe, Mar 01 2005

nonn

a(6), which corresponds to n=649, is too large to include.

Cf. A005725 (quadrinomial coefficients), A104314 (nontrivial prime pentanomial coefficients).

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}]

A104313 Numbers n such that the coefficient of x^(2n) in (x^4+x^3+x^2+x+1)^n is prime.

Original entry on oeis.org

2, 3, 28, 30, 31

Offset: 1

T. D. Noe, Mar 01 2005

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.

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, Apr 25 2005

Cf. A005191 (pentanomial coefficients).

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}]

cp's OEIS Frontend

A104312 Prime coefficient of x^n in (x^3+x^2+x+1)^n for n in A104311.

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