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

Author

Paul Vanderveen, Aug 10 2022

Keywords

• nonn

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

Examples

			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.
		

References

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

Programs

PARI

a(n)={K=bnfinit(polcyclo(23)); ct=0; p=1; while(ct0, ct++); ); return(p)}