A341249 - OEIS

A341249

a(n) = floor(r*floor(s*n)), where r = 2 + sqrt(2) and s = sqrt(2).

3, 6, 13, 17, 23, 27, 30, 37, 40, 47, 51, 54, 61, 64, 71, 75, 81, 85, 88, 95, 99, 105, 109, 112, 119, 122, 129, 133, 139, 143, 146, 153, 157, 163, 167, 170, 177, 180, 187, 191, 194, 201, 204, 211, 215, 221, 225, 228, 235, 238, 245, 249, 252, 259, 262, 269

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OFFSET

1,1

COMMENTS

Conjecture: 1 < r*s*n - a(n) < 2 for n >= 1.

LINKS

Table of n, a(n) for n=1..56.

MATHEMATICA

z = 140; r = 2 + Sqrt[2]; s = Sqrt[2]; f[x_] := Floor[r*Floor[s*x]];

Table[f[n], {n, 1, z}]

Table[Floor[(2+Sqrt[2])Floor[n Sqrt[2]]], {n, 60}] (* Harvey P. Dale, Oct 09 2022 *)

CROSSREFS