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A231614 Numbers n such that the five eighth-degree cyclotomic polynomials are simultaneously prime. 4
4069124, 8919014, 8942756, 46503870, 75151624, 82805744, 189326670, 197155324, 271490544, 365746304, 648120564, 1031944990 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The polynomials are cyclotomic(15,x) = 1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8, cyclotomic(16,x) = 1 + x^8, cyclotomic(20,x) = 1 - x^2 + x^4 - x^6 + x^8, cyclotomic(24,x) = 1 - x^4 + x^8, and cyclotomic(30,x) = 1 + x - x^3 - x^4 - x^5 + x^7 + x^8. The numbers 15, 16, 20, 24 and 30 are in the eighth row of A032447.

By Schinzel's hypothesis H, there are an infinite number of n that yield simultaneous primes. Note that the two first-degree cyclotomic polynomials, x-1 and x+1, yield the twin primes for the numbers in A014574.

REFERENCES

See A087277.

LINKS

Table of n, a(n) for n=1..12.

MATHEMATICA

t = {}; n = 0; While[Length[t] < 6, n++; If[PrimeQ[Cyclotomic[15, n]] && PrimeQ[Cyclotomic[16, n]] && PrimeQ[Cyclotomic[20, n]] && PrimeQ[Cyclotomic[24, n]] && PrimeQ[Cyclotomic[30, n]], AppendTo[t, n]]]; t

CROSSREFS

Cf. A014574 (first degree solutions: average of twin primes).

Cf. A087277 (similar, but with second-degree cyclotomic polynomials).

Cf. A231612 (similar, but with fourth-degree cyclotomic polynomials).

Cf. A231613 (similar, but with sixth-degree cyclotomic polynomials).

Sequence in context: A251614 A187599 A246470 * A191346 A307846 A278199

Adjacent sequences:  A231611 A231612 A231613 * A231615 A231616 A231617

KEYWORD

nonn,more

AUTHOR

T. D. Noe, Dec 11 2013

EXTENSIONS

Extended to 12 terms by T. D. Noe, Dec 13 2013

STATUS

approved

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Last modified September 20 01:41 EDT 2020. Contains 337249 sequences. (Running on oeis4.)