|
Search: id:A146334
|
|
|
| A146334 |
|
Numbers k such that continued fraction of (1+Sqrt[k])/2 has period 10 |
|
+0
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; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
For primes in this sequence see A146355.
|
|
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: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 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*)
|
|
CROSSREFS
|
A000290, A078370, A146326-A146345, A146348-A146360.
Sequence in context: A020349 A050959 A139917 this_sequence A039385 A043208 A043988
Adjacent sequences: A146331 A146332 A146333 this_sequence A146335 A146336 A146337
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Artur Jasinski (grafix(AT)csl.pl), Oct 30 2008
|
|
EXTENSIONS
|
284 removed by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 06 2009
|
|
|
Search completed in 0.002 seconds
|
