OFFSET
1,1
COMMENTS
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
REFERENCES
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).
LINKS
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.
PROG
(PARI) {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
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Term 3 added by Rick L. Shepherd, Apr 29 2015
STATUS
approved