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

Author

David Brink, Dec 29 2007

Keywords

• nonn
• fini

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

Crossrefs

Cf. A003173, A317987 (subsequence).

Programs

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