A090348 - OEIS

A090348

Norms of prime elements in the ring of integers of Q(sqrt(-7)).

2, 7, 9, 11, 23, 25, 29, 37, 43, 53, 67, 71, 79, 107, 109, 113, 127, 137, 149, 151, 163, 169, 179, 191, 193, 197, 211, 233, 239, 263, 277, 281, 289, 317, 331, 337, 347, 359, 361, 373, 379, 389, 401, 421, 431, 443, 449, 457, 463, 487, 491, 499

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OFFSET

1,1

COMMENTS

Consists of those primes in A045373 together with the squares of those primes not in A045373.

REFERENCES

A. Frohlich and M. J. Taylor, Algebraic number theory, Cambridge studies in advanced mathematics, no. 27, Cambridge University Press, 1991.

LINKS

Table of n, a(n) for n=1..52.

CROSSREFS

Cf. A175629 ({kronecker(-7,n)}), whose inverse Moebius transform A035182 gives the numbers of distinct ideals (or non-associate elements) with each norm (i.e., the coefficients of Dedekind zeta function).

The total numbers of elements with each norms are given by A002652.

Cf. A045373 (primes not inert in Q(sqrt(-7))), A045386 (primes decomposing), A003625 (primes remaining inert), A045399 (primes not decomposing).

Norms of prime ideals in the ring of integers of quadratic fields of class number 1: A391371 (D=24), A391370 (D=21), A391369 (D=12), A055673 (D=8), A341783 (D=5), A055664 (D=-3), A055025 (D=-4), this sequence (D=-7), A341784 (D=-8), A341785 (D=-11), A341787 (D=-19), A341788 (D=-43), A341789 (D=-67), A341790 (D=-163).

Norms of prime ideals in the ring of integers of quadratic fields of class number 2: A391367 (D=40), A341786 (D=-15), A091727 (D=-20), A391366 (D=-24).

Sequence in context: A288598 A277737 A082371 * A163405 A049638 A190490

Adjacent sequences: A090345 A090346 A090347 * A090349 A090350 A090351

KEYWORD

easy,nonn

AUTHOR

Paul Boddington, Jan 29 2004

STATUS

approved