A341788 Norms of prime elements in Z[(1+sqrt(-43))/2], the ring of integers of Q(sqrt(-43)).
4, 9, 11, 13, 17, 23, 25, 31, 41, 43, 47, 49, 53, 59, 67, 79, 83, 97, 101, 103, 107, 109, 127, 139, 167, 173, 181, 193, 197, 229, 239, 251, 269, 271, 281, 283, 293, 307, 311, 317, 337, 353, 359, 361, 367, 379, 397, 401, 431, 439, 443, 461, 479, 487, 509
Offset: 1
Examples
norm((1 + sqrt(-43))/2) = norm((1 - sqrt(-43))/2) = 11; norm((3 + sqrt(-43))/2) = norm((3 - sqrt(-43))/2) = 13; norm((5 + sqrt(-43))/2) = norm((5 - sqrt(-43))/2) = 17; norm((7 + sqrt(-43))/2) = norm((7 - sqrt(-43))/2) = 23; ... norm((19 + sqrt(-43))/2) = norm((19 - sqrt(-43))/2) = 101.
Links
- Jianing Song, Table of n, a(n) for n = 1..10000
Crossrefs
The number of nonassociative elements with norm n (also the number of distinct ideals with norm n) is given by A035147.
The total number of elements with norm n is given by A138811.
Norms of prime ideals in O_K, where K is the quadratic field with discriminant D and O_K be the ring of integers of K: A055673 (D=8), A341783 (D=5), A055664 (D=-3), A055025 (D=-4), A090348 (D=-7), A341784 (D=-8), A341785 (D=-11), A341786 (D=-15*), A341787 (D=-19), A091727 (D=-20*), this sequence (D=-43), A341789 (D=-67), A341790 (D=-163). Here a "*" indicates the cases where O_K is not a unique factorization domain.
Programs
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PARI
isA341788(n) = my(disc=-43); (isprime(n) && kronecker(disc,n)>=0) || (issquare(n, &n) && isprime(n) && kronecker(disc,n)==-1)
Comments