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 A146333 Numbers k such that continued fraction of (1 + sqrt(k))/2 has period 8. 3
 31, 40, 46, 71, 76, 88, 91, 92, 96, 104, 108, 152, 153, 155, 176, 188, 192, 200, 206, 207, 234, 238, 261, 266, 276, 279, 280, 282, 320, 328, 335, 336, 348, 366, 378, 383, 386, 392, 408, 414, 450, 476, 477, 480, 488, 501, 503, 504, 505, 540, 542, 555, 558, 581 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For primes in this sequence see A146353. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 EXAMPLE a(1) = 31 because continued fraction of (1+sqrt(31))/2 = 3, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, ... has period (3, 1, 1, 10, 1, 1, 3, 5) length 8. MAPLE A146326 := proc(n) if not issqr(n) then numtheory[cfrac]( (1+sqrt(n))/2, 'periodic', 'quotients') ; nops(%[2]) ; else 0 ; fi; end: isA146333 := proc(n) RETURN(A146326(n) = 8) ; end: for n from 2 to 700 do if isA146333(n) then printf("%d, ", n) ; fi; od: # R. J. Mathar, Sep 06 2009 MATHEMATICA s = 10; aa = {}; Do[k = ContinuedFraction[(1 + Sqrt[n])/2, 1000]; If[Length[k] < 190, AppendTo[aa, 0], m = 1; While[k[[s ]] != k[[s + m]] || k[[s + m]] != k[[s + 2 m]] || k[[s + 2 m]] != k[[s + 3 m]] || k[[s + 3 m]] != k[[s + 4 m]], m++ ]; s = s + 1; While[k[[s ]] != k[[s + m]] || k[[s + m]] != k[[s + 2 m]] || k[[s + 2 m]] != k[[s + 3 m]] || k[[s + 3 m]] != k[[s + 4 m]], m++ ]; s = s + 1; While[k[[s ]] != k[[s + m]] || k[[s + m]] != k[[s + 2 m]] || k[[s + 2 m]] != k[[s + 3 m]] || k[[s + 3 m]] != k[[s + 4 m]], m++ ]; AppendTo[aa, m]], {n, 1, 500}]; bb = {}; Do[If[aa[[n]] == 8, AppendTo[bb, n]], {n, 1, Length[aa]}]; bb (* Artur Jasinski *) cf8Q[n_]:=Module[{sqrt=Sqrt[n]}, !IntegerQ[sqrt]&&Length[ ContinuedFraction[ (1+sqrt)/2][[2]]]==8]; Select[Range[600], cf8Q] (* Harvey P. Dale, Sep 06 2012 *) CROSSREFS Cf. A000290, A078370, A146326-A146345, A146348-A146360. Sequence in context: A039378 A043201 A043981 * A109645 A156298 A099180 Adjacent sequences:  A146330 A146331 A146332 * A146334 A146335 A146336 KEYWORD nonn AUTHOR Artur Jasinski, Oct 30 2008 EXTENSIONS 155 and 279 etc. added, 311 etc. removed by R. J. Mathar, Sep 06 2009 STATUS approved

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Last modified July 23 04:00 EDT 2019. Contains 325230 sequences. (Running on oeis4.)