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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A087947 Sum of successive remainders in computing Euclidean algorithm for (1, 1/sqrt(-n)) has real and imaginary parts equal.

Original entry on oeis.org

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Offset: 1

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Author

Thomas Baruchel, Sep 07 2003

Keywords

Comments

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.
For all a(n) in the sequence, the relation: (2k)^2 <= a(n) <= (2k+1)^2 is true.

Examples

			kappa(1/sqrt(-203)) = (1/2 + (1/2)i) - (1/29 + (1/29)i)*sqrt(203).

Crossrefs

Cf. A086378, A087948.

Programs

  • MuPAD
    kappa_1_over_comp_sqrt := proc(n) local a,b,i,p; begin if (a := sqrt(-n)-isqrt(-n)) = 0 then return(0) end_if: a := simplify(1/a,sqrt); i := a := simplify(1/(a - floor(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((1-isqrt(n)/sqrt(n))*(1+b/(p-1)+1/a-floor(1/a)),sqrt)); end_proc:
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