A098021 Positions of 0's in the zero-one sequence [nr+2r]-[nr]-[2r], where r=sqrt(2) and [ ]=floor; see A187967.

5, 10, 17, 22, 29, 34, 39, 46, 51, 58, 63, 68, 75, 80, 87, 92, 99, 104, 109, 116, 121, 128, 133, 138, 145, 150, 157, 162, 169, 174, 179, 186, 191, 198, 203, 208, 215, 220, 227, 232, 237, 244, 249, 256, 261, 268, 273, 278, 285, 290, 297, 302, 307, 314, 319, 326

Offset: 1

Author

Roger L. Bagula, Sep 09 2004

Keywords

• nonn

Comments

Former definition was "Irrational rotation of the square root of 2 as an implicit sequence with an uneven Cantor cartoon." Replaced this with more precise definition from Clark Kimberling. - N. J. A. Sloane, Jan 30 2016

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A187967.

Programs

Magma

[3*n+2*Floor(n*Sqrt(2)): n in [1..60]]; // Vincenzo Librandi, Dec 17 2015

Mathematica

Table[7 Floor[n (Sqrt[2] - 1)] + 5 Floor[n (2 - Sqrt[2])] + 5, {n, 1000}] (* Miko Labalan, Dec 14 2015 *)
Table[3*n + 2*Floor[n*Sqrt[2]], {n,1,100}] (* G. C. Greubel, Mar 27 2018 *)

PARI

for(n=1,100, print1(3*n + 2*floor(n*sqrt(2)), ", ")) \\ G. C. Greubel, Mar 27 2018

Formula

a(n) = 7 * floor(n * (sqrt(2) - 1)) + 5 * floor(n * (2 - sqrt(2))) + 5. - Miko Labalan, Dec 14 2015

a(n) = 3*n + 2*floor(n*sqrt(2)). - G. C. Greubel, Mar 27 2018

Extensions

Edited and extended by Robert G. Wilson v, Sep 25 2004

Entry revised by N. J. A. Sloane, Jan 30 2016