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A065375
The next smallest pair of numbers is taken so that a(2n-1)/a(2n) converges to sqrt(2).
0
1, 1, 3, 2, 4, 3, 7, 5, 17, 12, 24, 17, 41, 29, 99, 70, 140, 99, 239, 169, 577, 408, 816, 577, 1393, 985, 3363, 2378, 4756, 3363, 8119, 5741, 19601, 13860, 27720, 19601, 47321, 33461, 114243, 80782, 161564, 114243, 275807, 195025, 665857, 470832, 941664, 665857, 1607521, 1136689, 3880899, 2744210
OFFSET
1,3
COMMENTS
"Next smallest" means that a(2n-1)+a(2n) is the smallest value that is greater than the previous pair.
EXAMPLE
abs(1/1-sqrt(2)) > abs(3/2-sqrt(2)) > abs(4/3-sqrt(2)) > abs(7/5-sqrt(2)) > abs(17/12-sqrt(2)) > ... > 0.
MATHEMATICA
AproximaRaiz2Vector[it_] := (
error = 1;
itactual = 0;
d = 1;
Lista = {};
While[itactual < it,
n = Floor[Sqrt[2]*d];
erroract = Abs[n/d - Sqrt[2]];
If[erroract < error, error = erroract; itactual++;
Print[n, "/", d, " = ", n/d + .0, " - E: ",
Abs[n/d - Sqrt[2]] + .0]; Lista = Append[Lista, n];
Lista = Append[Lista, d]];
n++;
erroract = Abs[n/d - Sqrt[2]];
If[erroract < error, error = erroract; itactual++;
Print[n, "/", d, " = ", n/d + .0, " - E: ",
Abs[n/d - Sqrt[2]] + .0]; Lista = Append[Lista, n];
Lista = Append[Lista, d]];
d++;
];
Lista
); (* Maximiliano Alba, Jan 19 2021 *)
CROSSREFS
Sequence in context: A024596 A262610 A175508 * A070961 A243291 A245962
KEYWORD
nonn
AUTHOR
Bodo Zinser, Nov 22 2001
EXTENSIONS
Corrected and extended by Maximiliano Alba, Jan 19 2021
STATUS
approved