A293504 The integer k that minimizes |k/n^2 - sqrt(2)|.

0, 1, 6, 13, 23, 35, 51, 69, 91, 115, 141, 171, 204, 239, 277, 318, 362, 409, 458, 511, 566, 624, 684, 748, 815, 884, 956, 1031, 1109, 1189, 1273, 1359, 1448, 1540, 1635, 1732, 1833, 1936, 2042, 2151, 2263, 2377, 2495, 2615, 2738, 2864, 2992, 3124, 3258

Offset

0,3

Links

Clark Kimberling, Table of n, a(n) for n = 0..1000

Formula

a(n) = floor(1/2 + (n^2)*sqrt(2)).

a(n) = A293502(n) if (fractional part of (sqrt(2))*n^2) < 1/2, else a(n) = A293503(n).

Mathematica

z = 120; r = Sqrt[2];
Table[Floor[r*n^2], {n, 0, z}];   (* A293502 *)
Table[Ceiling[r*n^2], {n, 0, z}]; (* A293503 *)
Table[Round[r*n^2], {n, 0, z}];   (* A293504 *)

Prog

(PARI) vector(100, n, n--; round(n^2*sqrt(2))) \\ G. C. Greubel, Aug 16 2018
(Magma) [Round(n^2*Sqrt(2)): n in [0..100]]; // G. C. Greubel, Aug 16 2018

Crossrefs

Cf. A002193, A293502, A293503.

Sequence in context: A236577 A356091 A359351 * A194126 A296310 A235450

Adjacent sequences: A293501 A293502 A293503 * A293505 A293506 A293507

Keyword

nonn,easy

Author

Clark Kimberling, Oct 12 2017

Status

approved