

A233512


The first n cyclotomic polynomials are simultaneously prime for these arguments.


1




OFFSET

1,1


COMMENTS

The first six cyclotomic polynomials are x  1, x + 1, x^2 + x + 1, x^2 + 1, x^4 + x^3 + x^2 + x + 1, and x^2  x + 1.
By Schinzel's hypothesis H, this sequence is defined for all n.
a(7) > 2*10^9.


REFERENCES

See A087277.


LINKS

Table of n, a(n) for n=1..6.


EXAMPLE

At x = 3, x1 = 2, which is prime. At x = 4, x1 = 3 and x+1 = 5, which are both prime. At x = 6, x1 = 5, x+1 = 7, and x^2+x+1 = 43, which are all prime.


MATHEMATICA

t = {}; n = 0; len = 0; While[len < 6, n++; found = True; i = 1; While[found && i <= len + 1, found = PrimeQ[Cyclotomic[i, n]]; i++]; If[found && i > len + 1, AppendTo[t, n]; len++]]; 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).
Cf. A231614 (similar, but with eighthdegree cyclotomic polynomials).
Sequence in context: A066466 A332511 A129293 * A095877 A024476 A173014
Adjacent sequences: A233509 A233510 A233511 * A233513 A233514 A233515


KEYWORD

nonn,hard,more


AUTHOR

T. D. Noe, Dec 13 2013


STATUS

approved



