A293502 Greatest integer k such that k/n^2 < sqrt(2).

0, 1, 5, 12, 22, 35, 50, 69, 90, 114, 141, 171, 203, 239, 277, 318, 362, 408, 458, 510, 565, 623, 684, 748, 814, 883, 956, 1030, 1108, 1189, 1272, 1359, 1448, 1540, 1634, 1732, 1832, 1936, 2042, 2151, 2262, 2377, 2494, 2614, 2737, 2863, 2992, 3123, 3258

Offset

0,3

Links

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

Formula

a(n) = floor(r*n^2), where r = sqrt(2).

a(n) = A293503(n) - 1 for n > 0.

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

Crossrefs

Cf. A002193, A293503, A293504.

Sequence in context: A333578 A131976 A074376 * A134340 A000326 A022795

Adjacent sequences: A293499 A293500 A293501 * A293503 A293504 A293505

Keyword

nonn,easy

Author

Clark Kimberling, Oct 11 2017

Status

approved