A146334 Numbers k such that continued fraction of (1 + sqrt(k))/2 has period 10.
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
Offset: 1
Keywords
Examples
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.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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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
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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 *)
Extensions
284 removed by R. J. Mathar, Sep 06 2009
Comments