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 A070519 #37 Feb 16 2025 08:32:46
%S A070519 2,3,4,6,10,12,14,19,31,46,74,75,98,102,126,180,236,310,368,1770,1858,
%T A070519 3512,4878,5730,7547,7990,8636,9378,11262
%N A070519 Numbers k such that Cyclotomic(k,k) (i.e., the value of k-th cyclotomic polynomial at k) is a prime number.
%C A070519 When n is prime, then the solutions are given in A088790.
%C A070519 No term of this sequence is congruent to 1 mod 4. In general, if k = s^2*t where t is squarefree and t == 1 (mod 4), then Cyclotomic(k,t*x^2) is the product of two polynomials. See the Wikipedia link below. - _Jianing Song_, Sep 25 2019
%C A070519 All terms <= 1858 have been proven with PARI's implementation of ECPP. All larger terms are BPSW PRPs. There are no further terms <= 30000. - _Lucas A. Brown_, Dec 28 2020
%H A070519 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CyclotomicPolynomial.html">Cyclotomic Polynomial</a>
%H A070519 Wikipedia, <a href="https://en.wikipedia.org/wiki/Aurifeuillean_factorization">Aurifeuillean factorization</a>
%t A070519 Do[s=Cyclotomic[n, n]; If[PrimeQ[s], Print[n]], {n, 2, 256}]
%o A070519 (PARI) for(n=2,10^9,if(ispseudoprime(polcyclo(n,n)),print1(n,", "))); \\ _Joerg Arndt_, Jan 22 2015
%Y A070519 Cf. A070518, A070520, A088790 ((k^k-1)/(k-1) is prime), A088817 (cyclotomic(2k,k) is prime), A088875 (cyclotomic(k,-k) is prime).
%Y A070519 Cf. A117544, A085398.
%K A070519 nonn,more
%O A070519 1,1
%A A070519 _Labos Elemer_, May 02 2002
%E A070519 More terms from _T. D. Noe_, Oct 17 2003
%E A070519 a(29) from _Charles R Greathouse IV_, May 05 2011