OFFSET

1,1

COMMENTS

Primes which are norms of principal ideals in the 23rd cyclotomic ring of integers.

The class number of the 23rd cyclotomic field is 3, so about 1/3 of primes == 1 (mod 23) should be norms of principal ideals.

Is it true that a(n) == 1 (mod 46)? - Hugo Pfoertner, Aug 13 2022

REFERENCES

Reimer Bruchmann, Quadratic and cyclotomic rings of integers, March 26th, 2022, 487-534.

EXAMPLE

2347 is in this sequence since it is the norm of the element x^7-x^3-x-1 where x is a 23rd primitive root of unity.

PROG

(PARI) a(n)={K=bnfinit(polcyclo(23)); ct=0; p=1; while(ct<n, p=nextprime(p+1); if(p%23==1 && #bnfisintnorm(K, p)>0, ct++); ); return(p)}

CROSSREFS

KEYWORD

nonn

AUTHOR

Paul Vanderveen, Aug 10 2022

STATUS

approved