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Search: id:A146343
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| A146343 |
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a(n) = smallest number k such that continued fraction of (1+Sqrt[k])/2 has period length n. |
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+0
3
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| 5, 2, 17, 6, 41, 18, 89, 31, 73, 43, 265, 94, 421, 118, 193, 172, 521, 106, 241, 151, 337, 489, 433, 268, 929, 211, 409, 334, 673, 379
(list; graph; listen)
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OFFSET
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1,1
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MAPLE
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A := proc(n) local c; try c := numtheory[cfrac](1/2+sqrt(n)/2, 'periodic', 'quotients') ; RETURN(nops(c[2]) ); catch: RETURN(-1) end try ; end: A146343 := proc(n) for k from 1 do if A(k) = n then RETURN(k); fi; od: end: for n from 1 to 30 do printf("%d, ", A146343(n)) ; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 08 2008]
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MATHEMATICA
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$MaxExtraPrecision = 300; 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++ ]; AppendTo[aa, m]], {n, 1, 1200}]; Print[aa]; bb = {}; Do[k = 1; yes = 0; Do[If[aa[[k]] == n && yes == 0, AppendTo[bb, k]; yes = 1], {k, 1, Length[aa]}], {n, 1, 22}]; bb (*Artur Jasinski*)
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CROSSREFS
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A000290, A078370, A146326-A146345, A146348-A146360.
Sequence in context: A060422 A128142 A111267 this_sequence A146363 A087958 A130329
Adjacent sequences: A146340 A146341 A146342 this_sequence A146344 A146345 A146346
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Oct 30 2008
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EXTENSIONS
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a(6) changed to 18, a(25) to 929, a(28) to 334 by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 08 2008
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