This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A231614 #5 Dec 13 2013 12:34:19
%S A231614 4069124,8919014,8942756,46503870,75151624,82805744,189326670,
%T A231614 197155324,271490544,365746304,648120564,1031944990
%N A231614 Numbers n such that the five eighth-degree cyclotomic polynomials are simultaneously prime.
%C A231614 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.
%C A231614 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.
%D A231614 See A087277.
%t A231614 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
%Y A231614 Cf. A014574 (first degree solutions: average of twin primes).
%Y A231614 Cf. A087277 (similar, but with second-degree cyclotomic polynomials).
%Y A231614 Cf. A231612 (similar, but with fourth-degree cyclotomic polynomials).
%Y A231614 Cf. A231613 (similar, but with sixth-degree cyclotomic polynomials).
%K A231614 nonn,more
%O A231614 1,1
%A A231614 _T. D. Noe_, Dec 11 2013
%E A231614 Extended to 12 terms by _T. D. Noe_, Dec 13 2013