A260335 -id:A260335 - cp's OEIS frontend

3, 7, 11, 19, 23, 31, 43, 47, 59, 67, 71, 83, 103, 107, 127, 131, 139, 151, 163, 167, 179, 191, 199, 211, 227, 239, 251, 263, 271, 283, 307, 311, 331, 347, 367, 379, 383, 419

Offset: 1

N. J. A. Sloane

nonn

The Suryanarayana paper contains these errors: In section 2, list (1) omits 3 and an asterisk should follow 1987; list (2) should include neither 3203 nor 3271. Section 3 should say "Of the 339 primes d == 3 (4) up to 5000, 289 primes satisfy h(d) = 2, while 50 do not." (correcting all three counts) - Rick L. Shepherd, Apr 29 2015

Also primes p > 2 such that Z[sqrt(p)] = Z[x]/(x^2 - p) is a unique factorization domain (or equivalently, a principal ideal domain). This can be deduced from the following result: let K be the quadratic field with discriminant D > 0, h(D) and h_+(D) be the ordinary class number and narrow class numer (or form class number) of K respectively, then h_+(D)/h(D) = 1 if the fundamental unit of K has norm -1; 2 if the fundamental unit of K has norm 1. - Jianing Song, Feb 17 2021

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Rick L. Shepherd, Table of n, a(n) for n = 1..10000
M. Suryanarayana, Positive determinants of binary quadratic forms whose class-number is 2, Proceedings of the Indian Academy of Sciences. Section A, 2 (1935), 178-179.

Cf. A260335. Subsequence of A002145.

{QFBclassno(D) = qfbclassno(D) * if(D < 0 || norm(quadunit(D)) < 0, 1, 2);
n=0; forprime(p=3, 291619, if(p%4 == 3 && QFBclassno(4*p) == 2, n++; write("b002052.txt", n, " ", p)))} \\ Rick L. Shepherd, Apr 29 2015

Term 3 added by Rick L. Shepherd, Apr 29 2015

cp's OEIS Frontend

A002052 Prime determinants of forms with class number 2.

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