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A087948
Sum of successive remainders in computing euclidean algorithm for (1, -1/sqrt(-n)) has real and imaginary parts equal.
1
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
OFFSET
1,2
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.
EXAMPLE
kappa(-1/sqrt(-105)) = -(1/210 + (1/210)i)*sqrt(105).
PROG
(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:
CROSSREFS
Sequence in context: A049860 A010382 A138673 * A010437 A020682 A243702
KEYWORD
nonn
AUTHOR
Thomas Baruchel, Sep 07 2003
STATUS
approved