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 A355461 Squarefree numbers d of the form r^2*m^2 + 4*r, where r and m are odd positive integers, such that Q(sqrt(d)) has class number 1. 0
 5, 13, 21, 29, 53, 173, 237, 293, 437, 453, 1133, 1253 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS In 1801, Gauss conjectured that there exist infinitely many real quadratic fields with class number one and the conjecture is still unproved, but there are only 12 real quadratic fields of class number one which are of the form Q(sqrt(r^2*m^2 + 4*r)), where the parameters r and m are odd integers. Those 12 values of d := r^2*m^2 + 4*r belong to the present sequence. LINKS A. Biró and K. Lapkova The class number one problem for the real quadratic fields Q(sqrt(a*n^2+4*a)), Acta Arith., vol. 172(2), 2016, pp. 117-131. A. Hoque and S. Kotyada Class number one problem for the real quadratic fields Q(sqrt(m^2+2*r)), Archiv der Mathematik, vol. 116(1), 2021, pp. 33-36. EXAMPLE a(2) = 13 since h(13) = h(1^2*3^2 + 4*1) = 1. CROSSREFS Cf. A050950, A053329, A308420. Sequence in context: A191155 A107996 A107997 * A166095 A166090 A065766 Adjacent sequences: A355458 A355459 A355460 * A355462 A355463 A355464 KEYWORD nonn,fini,full AUTHOR Marco Ripà, Jul 02 2022 STATUS approved

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Last modified March 31 08:44 EDT 2023. Contains 361645 sequences. (Running on oeis4.)