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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

"Next smallest" means that a(2n-1)+a(2n) is the smallest value that is greater than the previous pair.

LINKS

Table of n, a(n) for n=1..52.

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

Adjacent sequences:  A065372 A065373 A065374 * A065376 A065377 A065378

KEYWORD

nonn

AUTHOR

Bodo Zinser, Nov 22 2001

EXTENSIONS

Corrected and extended by Maximiliano Alba, Jan 19 2021

STATUS

approved

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Last modified December 7 07:24 EST 2021. Contains 349567 sequences. (Running on oeis4.)