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 A356467 #11 Jul 15 2023 10:36:23
%S A356467 7,11,29,23,53,103,191,599,4931,5953,32783,101107,178021,549149
%N A356467 Smallest prime congruent to 1 (mod prime(n)) which is the norm of some principal ideal in the ring of prime(n)-th cyclotomic integers.
%C A356467 For the p-th cyclotomic ring of integers, primes which are norms of principal ideals should have asymptotic density 1/(h(p)*(p-1)) where h(p) is the class number of the p-th cyclotomic field.
%e A356467 a(3) = 11 since 11 is the smallest prime congruent to 1 mod 5 (prime(3) = 5), which is the norm of some element in the 5th cyclotomic ring of integers. The algebraic integer x^2-x-1 has norm 11 where x is a primitive 5th root of unity.
%e A356467 a(2) - a(8) are the smallest primes congruent to 1 mod prime(n) as those corresponding cyclotomic fields have class number 1.
%e A356467 a(9) = 599. The 23rd cyclotomic ring of integers does not have class number 1. The smallest prime congruent to 1 (mod 23) is 47, and there is no cyclotomic integer with norm 47. The algebraic integer x^3-x-1 has norm 599 where x is a primitive 23rd root of unity.
%o A356467 (PARI) a(n)={ p=prime(n); t=0; K=bnfinit(polcyclo(p)); q=1; while(t==0, q=nextprime(q+1); if(q%p==1 && #bnfisintnorm(K,q)>0, t=1); ); return(q); }
%Y A356467 Cf. A035095.
%K A356467 nonn,more
%O A356467 2,1
%A A356467 _Paul Vanderveen_, Aug 08 2022