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

1,1

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