A104312 -id:A104312 - cp's OEIS frontend

A104314 Prime coefficient of x^(2*k) in (x^4 + x^3 + x^2 + x + 1)^k for k in A104313.

5, 19, 1974442362935339179, 47705925773278538281, 234692178470218983001

Offset: 1

T. D. Noe, Mar 01 2005

nonn

a(6) > A005191(195315), if it exists. See A104313 for more information. - Jinyuan Wang, Jul 26 2021

Cf. A005191 (pentanomial coefficients), A104312 (nontrivial prime quadrinomial coefficients), 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}]

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

Original entry on oeis.org

2, 4, 5, 8, 73, 649

Offset: 1

T. D. Noe, Mar 01 2005

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

Cf. A005725 (quadrinomial 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}]

cp's OEIS Frontend

A104314 Prime coefficient of x^(2*k) in (x^4 + x^3 + x^2 + x + 1)^k for k in A104313.

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