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Search: id:A087948
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| A087948 |
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Sum of successive remainders in computing euclidean algorithm for (1,-1/sqrt(-n)) has real and imaginary parts equal. |
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+0
2
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| 1, 4, 5, 9, 16, 17, 18, 25, 36, 37, 39, 49, 64, 65, 66, 68, 81, 100, 101, 105, 121, 126, 144, 145, 146, 147, 150, 169, 196, 197, 203, 225, 256, 257, 258, 260, 264, 289, 324, 325, 327, 333, 361, 400, 401, 402, 405, 410, 441, 484, 485, 495, 529, 576, 577, 578, 579
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Since the computation of the algorithm needs an extension of the integer part over a subset of C, the rule: floor(I*x)=I*floor(x) is used (which is what MuPAD does). The following program computes the exact value of the sum.
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EXAMPLE
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kappa(-1/sqrt(-105)) = -(1/210 + 1/210 I).sqrt(105).
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PROGRAM
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(MuPAD) kappa_neg_1_over_comp_sqrt := proc(n) local a, b, i, p; begin if (a := -sqrt(-n)+ceil(sqrt(-n))) = 0 then return(0) end_if: i := a := simplify(1/a, sqrt); p := 1; b := 0; repeat p := p*a; b := b*a+a-floor(a); until (a := simplify(1/(a-floor(a)), sqrt)) = i end_repeat: return(simplify(-(b/(p-1) + 1/a)/sqrt(-n), sqrt)); end_proc:
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CROSSREFS
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Cf. A086378, A087947.
Sequence in context: A049860 A010382 A138673 this_sequence A010437 A020682 A155565
Adjacent sequences: A087945 A087946 A087947 this_sequence A087949 A087950 A087951
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KEYWORD
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nonn
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AUTHOR
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Thomas Baruchel (baruchel(AT)users.sourceforge.net), Sep 07 2003
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