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 A244658 a(n) = x/(x1-floor(x1)) where x = sqrt(n) - floor(sqrt(n)), x1 = 1/x, a(n) = -1 if division by zero, a(n) = 0 for nonintegers. 2
 -1, 1, 2, -1, 1, 2, 0, 4, -1, 1, 2, 3, 0, 0, 6, -1, 1, 2, 0, 4, 0, 0, 0, 8, -1, 1, 2, 0, 0, 5, 0, 0, 0, 0, 10, -1, 1, 2, 3, 4, 0, 6, 0, 0, 0, 0, 0, 12, -1, 1, 2, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 14, -1, 1, 2, 0, 4, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 16, -1, 1, 2, 3, 0, 0, 6, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 18, -1, 1, 2, 0, 4, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Inspired by the square root of three poem in "Harold and Kumar" the movie. This operation can be done in iterations for which some n seem to give all integer results after iteration k >= 2. Some of them have periodic properties similar to that of the continued fraction method (but not exactly the same). When a(n) is arranged as a table read by rows, the row sums would be A062731. See illustrations in links. LINKS Table of n, a(n) for n=1..105. Kival Ngaokrajang, Illustration for n = 1..20 and iteration k = 1..10   a(n) arrange as table for n = 1..168 answers.yahoo, What are the words to the math poem in "Harold and Kumar"? Eric Weisstein's World of Mathematics, Periodic Continued Fraction EXAMPLE For n = 3, x = sqrt(3) - floor(sqrt(3)) = 0.732050807..., x1 = 1/x = 1/0.732050807... = 1.366025403..., x1 - floor(x1) = 0.366025403..., a(3) = 0.732050807.../0.366025402... = 2. PROG (Small Basic) For n=1 To 500 x=math.Power(n, .5) y=x-math.Floor(x) If y<>0 Then x1=1/y x2=1/(x1-math.Floor(x1)) a1=x2/x1 a2=a1-math.floor(a1) If a2 > 0.999999 or a2 < 0.0000001 then a=math.Round(a1) TextWindow.Write(a+", ") Else TextWindow.Write(0+", ")'noninteger Endif Else TextWindow.Write(-1+", ")'zero division, Square number EndIf EndFor CROSSREFS Cf. A062731. Sequence in context: A088226 A344309 A358338 * A117586 A307988 A268917 Adjacent sequences: A244655 A244656 A244657 * A244659 A244660 A244661 KEYWORD sign AUTHOR Kival Ngaokrajang, Jul 04 2014 STATUS approved

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