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A143577
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Numbers k such that continued fraction of (1+Sqrt[k])/2 has period 9
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1
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73, 97, 233, 277, 349, 353, 613, 821, 877, 1073, 1181, 1189, 1277, 1285, 1313, 1385, 1613, 1637, 1693, 1745, 1865, 2357, 2581, 2777, 3233, 3557, 3989, 4157, 4469, 4517, 4553, 4709, 4889, 4925, 4933
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Something has gone wrong here - this is a subset of A146354. - N. J. A. Sloane (njas(AT)research.att.com), Oct 31 2008
For primes in this sequence see A146354.
Superset of A146354. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 05 2008]
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EXAMPLE
| a(1) = 73 because continued fraction of (1+Sqrt[73])/2 = 4, 1, 3, 2, 1, 1, 2, 3, 1, 7, 1, 3, 2, 1, 1, 2, 3, 1, 7, 1, 3, 2, 1, 1, 2, 3, 1, 7, 1, 3, ...
has period (1, 3, 2, 1, 1, 2, 3, 1, 7) length 9
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MAPLE
| isA143577 := proc(k) local c; try c := numtheory[cfrac](1/2+sqrt(k)/2, 'periodic', 'quotients') ; if nops(c[2]) = 9 then RETURN(true) ; else RETURN(false) ; fi; catch: RETURN(false) ; end try; end: for k from 2 to 80000 do if isA143577(k) then printf("%d, ", k) ; fi; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 05 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]] == 9, AppendTo[bb, n]], {n, 1, Length[aa]}]; bb (*Artur Jasinski*)
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CROSSREFS
| A000290, A078370, A146326-A146345, A146348-A146360.
Sequence in context: A141375 A107008 A140621 * A146354 A050958 A139990
Adjacent sequences: A143574 A143575 A143576 * A143578 A143579 A143580
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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
| Extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 05 2008
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