A133676 Negative discriminants with form class group of exponent 4 (negated).

39, 55, 56, 63, 68, 80, 128, 136, 144, 155, 156, 171, 184, 196, 203, 208, 219, 220, 224, 252, 256, 259, 260, 264, 275, 276, 291, 292, 308, 320, 323, 328, 336, 355, 360, 363, 384, 387, 388, 400, 456, 468, 475, 504, 507, 528, 544, 552, 564, 568, 576, 580, 592

Offset

1,1

Comments

The sequence is finite. It appears to have exactly 485 terms, the largest being 887040.

The finiteness of the sequence was proved by Earnest and Estes.

I found the 485 terms with PARI and didn't find any other up to 50000000.

Links

David Brink, Table of n, a(n) for n = 1..485

David Brink, Five peculiar theorems on simultaneous representation of primes by quadratic forms (Video abstract)

David Brink, Five peculiar theorems on simultaneous representation of primes by quadratic forms, J. Number Theory 129 (2009), no. 2, 464-468.

A. G. Earnest and D. R. Estes, An algebraic approach to the growth of class numbers of binary quadratic lattices, Mathematika 28 (1981), no. 2, 160--168.

Journal of Number Theory, Video Abstracts

Prog

(PARI) a(n) = if(n%4==0 || n%4==3, my(v = quadclassunit(-n)[2]); (#v > 0) && (v[1] == 4), 0) \\ Jianing Song, Sep 24 2022

Crossrefs

Cf. A003173, A317987 (subsequence).

Sequence in context: A252719 A252720 A070145 * A317987 A330219 A013658

Adjacent sequences: A133673 A133674 A133675 * A133677 A133678 A133679

Keyword

nonn,fini

Author

David Brink, Dec 29 2007

Status

approved