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 A146334 Numbers k such that continued fraction of (1 + sqrt(k))/2 has period 10. 2
 43, 67, 116, 129, 134, 161, 162, 184, 218, 242, 243, 246, 270, 274, 297, 301, 314, 338, 339, 345, 354, 356, 407, 411, 451, 452, 459, 465, 475, 498, 515, 517, 532, 534, 561, 563, 590, 591, 595, 597, 603, 611, 638, 648, 657, 665, 669, 671, 690, 705, 715 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For primes in this sequence see A146355. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE a(1) = 43 because continued fraction of (1+Sqrt[43])/2 = 3, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, ... has period (1, 3, 1, 1, 12, 1, 1, 3, 1, 5) length 10. MAPLE A146326 := proc(n) if not issqr(n) then numtheory[cfrac]( (1+sqrt(n))/2, 'periodic', 'quotients') ; nops(%[2]) ; else 0 ; fi; end: isA146334 := proc(n) RETURN(A146326(n) = 10) ; end: for n from 2 to 715 do if isA146334(n) then printf("%d, ", n) ; fi; od: # R. J. Mathar, Sep 06 2009 MATHEMATICA cf10Q[n_]:=Module[{s=(1+Sqrt[n])/2, x}, x=If[IntegerQ[s], 1, Length[ ContinuedFraction[ s][[2]]]]; x==10]; Select[Range[750], cf10Q] (* Harvey P. Dale, Sep 22 2015 *) CROSSREFS Cf. A000290, A078370, A146326-A146345, A146348-A146360. Sequence in context: A050959 A273773 A139917 * A039385 A043208 A043988 Adjacent sequences: A146331 A146332 A146333 * A146335 A146336 A146337 KEYWORD nonn AUTHOR Artur Jasinski, Oct 30 2008 EXTENSIONS 284 removed by R. J. Mathar, Sep 06 2009 STATUS approved

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Last modified July 25 08:50 EDT 2024. Contains 374587 sequences. (Running on oeis4.)