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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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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, 937, 463, 601, 331, 769, 721, 2297, 619, 1033, 718, 1777, 394, 1753, 604, 1993, 634, 1249, 526, 3649, 694
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..1000
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MAPLE
| 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
| nn = 50; t = Table[0, {nn}]; cnt = 0; k = 1; While[cnt < nn, k++; cf = ContinuedFraction[(1 + Sqrt[k])/2]; If[Head[cf[[-1]]] === List, len = Length[cf[[-1]]]; If[len <= nn && t[[len]] == 0, t[[len]] = k; cnt++]]]; t
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CROSSREFS
| Cf. A000290, A078370, A146326-A146345, A146348-A146360.
Sequence in context: A191435 A128142 A111267 * A146363 A087958 A189746
Adjacent sequences: A146340 A146341 A146342 * A146344 A146345 A146346
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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
| 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
Extended by T. D. Noe (noe(AT)sspectra.com), Mar 22 2011
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