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A104313 Numbers n such that the coefficient of x^(2n) in (x^4+x^3+x^2+x+1)^n is prime. 1
2, 3, 28, 30, 31 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..5.

MATHEMATICA

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}]

CROSSREFS

Cf. A005191 (pentanomial coefficients).

Sequence in context: A032813 A337560 A333704 * A279505 A279995 A279600

Adjacent sequences:  A104310 A104311 A104312 * A104314 A104315 A104316

KEYWORD

more,nonn

AUTHOR

T. D. Noe, Mar 01 2005

STATUS

approved

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Last modified October 23 20:31 EDT 2021. Contains 348215 sequences. (Running on oeis4.)