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A146334 Numbers k such that continued fraction of (1 + sqrt(k))/2 has period 10. 1
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

Table of n, a(n) for n=1..51.

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

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]] == 10, AppendTo[bb, n]], {n, 1, Length[aa]}]; bb (* Artur Jasinski *)

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 October 23 17:32 EDT 2019. Contains 328373 sequences. (Running on oeis4.)