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A146337
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Numbers k such that continued fraction of (1+Sqrt[k])/2 has period 14
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2
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118, 154, 179, 201, 212, 244, 251, 262, 286, 292, 307, 340, 347, 388, 403, 418, 422, 430, 467, 471, 474, 494, 497, 500, 519, 543, 548, 566, 587, 594, 598, 670, 683, 687, 692, 698, 699, 703, 713, 722, 742, 745, 754, 831, 833, 847, 873, 879, 932, 939, 945
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| For primes in this sequence see A146359.
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EXAMPLE
| a(1) = 421 because continued fraction of (1+Sqrt[421])/2 = 17, 5, 3, 1, 1, 1, 2, 26, 2, 1, 1, 1, 3, 5, 13, 5, 3, 1, 1, 1, 2, 26, 2, 1, 1, 1, 3, 5, 13, 5, 3, 1, 1, 1, 2, 26...
has period (5, 3, 1, 1, 1, 2, 26, 2, 1, 1, 1, 3, 5, 13) length 14
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MAPLE
| A := proc(n) option remember ; local c; try c := numtheory[cfrac](1/2+sqrt(n)/2, 'periodic', 'quotients') ; RETURN(nops(c[2]) ); catch: RETURN(-1) end try ; end: isA146337 := proc(n) if A(n) = 14 then RETURN(true); else RETURN(false); fi; end: for k from 1 do if isA146337(k) then printf("%d, ", k) ; fi; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 08 2008]
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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]] == 14, AppendTo[bb, n]], {n, 1, Length[aa]}]; bb (*Artur Jasinski*)
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CROSSREFS
| A000290, A078370, A146326-A146345, A146348-A146360.
Sequence in context: A039556 A095627 A066734 * A165462 A175876 A165156
Adjacent sequences: A146334 A146335 A146336 * A146338 A146339 A146340
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KEYWORD
| nonn
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Oct 30 2008
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 08 2008
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