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Search: id:A086882
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| A086882 |
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a(n) is the period of the imaginary continued fraction expansion of sqrt(-n). |
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+0
1
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| 0, 0, 2, 2, 0, 4, 4, 5, 4, 0, 6, 6, 6, 10, 8, 6, 0, 8, 8, 10, 8, 10, 12, 11, 8, 0, 10, 10, 12, 16, 10, 17, 11, 12, 14, 10, 0, 12, 12, 12, 12, 16, 12, 16, 16, 16, 26, 17, 12, 0, 14, 14, 16, 22, 16, 16, 14, 16, 20, 18, 16, 36, 20, 14, 0, 16, 16, 22, 16, 26, 18, 27, 16, 30, 20, 17, 26, 22
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Numbers n for which a(n) is odd seem to be a subset of numbers n for which A003285(n) is a multiple of 4. - Thomas Baruchel (baruchel(AT)users.sourceforge.net), Jul 03 2007
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EXAMPLE
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a(7) = 5 because sqrt(-7) = [2i, -2i, {-3i, -2i, -2i, -2i, -3i},...].
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PROGRAM
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(PARI) complex_period(n)= { local(a, b, c, d, k, oa, oc, i, s); s=sqrtint(n); if(issquare(c=n), 0, until(c==oc, oc=c; oa=a; if((a = (n-b^2)/c) == oa, return(2*i)); i += (k = (s-b)\a); d = a*k+b; c = (n-d^2)/a; b = (s+d)%c-s); 2*i-k); }
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CROSSREFS
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Cf. A003285.
Sequence in context: A078029 A078030 A073469 this_sequence A100240 A072690 A108520
Adjacent sequences: A086879 A086880 A086881 this_sequence A086883 A086884 A086885
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KEYWORD
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easy,nonn
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AUTHOR
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Thomas Baruchel (baruchel(AT)users.sourceforge.net), Aug 22 2003
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EXTENSIONS
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Edited by Don Reble (djr(AT)nk.ca), Jul 31 2006
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