A356531 Primes p == 1 (mod 23) which are norms of elements in the 23rd cyclotomic field.

599, 691, 829, 1151, 2347, 2393, 3037, 3313, 3359, 4463, 4831, 5107, 5521, 5659, 6763, 8741, 9109, 9661, 10627, 10949, 11593, 12743, 13249, 14537, 14767, 14951, 15319, 15733, 16883, 17573

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.

Links

Table of n, a(n) for n=1..30.

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

Sequence in context: A095746 A135846 A035209 * A385191 A385188 A135847

Adjacent sequences: A356528 A356529 A356530 * A356532 A356533 A356534

Keyword

nonn

Author

Paul Vanderveen, Aug 10 2022

Status

approved