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Search: id:A065014
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| A065014 |
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Least integer for which the periodic part of the continued fraction for its square root begins with n. |
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+0
1
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| 3, 2, 11, 5, 27, 10, 51, 17, 83, 26, 123, 37, 171, 50, 227, 65, 291, 82, 363, 101, 443, 122, 531, 145, 627, 170, 731, 197, 843, 226, 963, 257, 1091, 290, 1227, 325, 1371, 362, 1523, 401, 1683, 442, 1851, 485, 2027, 530, 2211, 577, 2403, 626, 2603, 677
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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G.f.: (x^5+3x^4-x^3+2x^2+2x+3)/(1-x^2)^3.
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EXAMPLE
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a(3) = 11 because the continued fraction for the square root of 11 is 3, {3, 6}.
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MATHEMATICA
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a = Table[0, {70}]; Do[ b = First[ Last[ ContinuedFraction[ Sqrt[ n]]]]; If[ b < 71 && a[[b]] == 0, a[[b]] = n], {n, 2, 10^4} ]; a
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CROSSREFS
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Cf. A013945. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 02 2008]
Sequence in context: A110326 A112061 A013945 this_sequence A072656 A163841 A072634
Adjacent sequences: A065011 A065012 A065013 this_sequence A065015 A065016 A065017
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KEYWORD
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cofr,easy,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 01 2001
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