

A231614


Numbers n such that the five eighthdegree cyclotomic polynomials are simultaneously prime.


4



4069124, 8919014, 8942756, 46503870, 75151624, 82805744, 189326670, 197155324, 271490544, 365746304, 648120564, 1031944990
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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 firstdegree cyclotomic polynomials, x1 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 seconddegree cyclotomic polynomials).
Cf. A231612 (similar, but with fourthdegree cyclotomic polynomials).
Cf. A231613 (similar, but with sixthdegree 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



