Search: id:A013643
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%I A013643
%S A013643 41,130,269,370,458,697,986,1313,1325,1613,1714,2153,2642,2834,3181,
%T A013643 3770,4409,4778,4933,5098,5837,5954,6626,7465,7610,8354,9293,10282,
%U A013643 10865,11257,11321,12410,13033,13549,14698,14738,15977,17266,17989
%N A013643 Numbers n such that continued fraction for sqrt(n) has period 3.
%C A013643 All numbers of the form (5n+1)^2 + 4n + 1 for n>0 are elements of this 
               sequence. Numbers of the above form have the continued fraction expansion 
               [5n+1,[2,2,10n+2]]. General square roots of integers with period 
               3 continued fraction expansions have expansions of the form [n,[2m,
               2m,2n]]. - David Terr (David_C_Terr(AT)raytheon.com), Jun 15 2004
%D A013643 Kenneth H. Rosen, Elementary Number Theory and Its Applications, Addison-Wesley, 
               1984, page 426 (but beware of errors in this reference!)
%F A013643 The general form of these numbers is d = d(m, n) = a^2 + 4mn + 1, where 
               m and n are positive integers and a = a(m, n) = (4m^2 + 1)n + m, 
               for which the continued fraction expansion of sqrt(d) is [a;[2m, 
               2m, 2a]]. - David Terr (David_C_Terr(AT)raytheon.com), Jul 20 2004
%Y A013643 Cf. A044292 A044673 A067896 A028343 A044373 A044754.
%Y A013643 Sequence in context: A135792 A067896 A142290 this_sequence A142333 A028343 
               A165816
%Y A013643 Adjacent sequences: A013640 A013641 A013642 this_sequence A013644 A013645 
               A013646
%K A013643 nonn
%O A013643 1,1
%A A013643 N. J. A. Sloane (njas(AT)research.att.com), Clark Kimberling (ck6(AT)evansville.edu), 
               Walter Gilbert

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