A187393 a(n) = floor(r*n), where r = 4 + sqrt(8); complement of A187394.

6, 13, 20, 27, 34, 40, 47, 54, 61, 68, 75, 81, 88, 95, 102, 109, 116, 122, 129, 136, 143, 150, 157, 163, 170, 177, 184, 191, 198, 204, 211, 218, 225, 232, 238, 245, 252, 259, 266, 273, 279, 286, 293, 300, 307, 314, 320, 327, 334, 341, 348, 355, 361, 368, 375, 382, 389, 396, 402, 409, 416, 423, 430, 437, 443, 450, 457, 464, 471, 477

Offset: 1

Author

Clark Kimberling, Mar 09 2011

Keywords

• nonn

Comments

A187393 and A187394 are the Beatty sequences for r = 4 + sqrt(8) and s = 4 - sqrt(8); 1/r + 1/s = 1.

Let u = 1 + sqrt(2) and v = -1 + sqrt(2). Let U = {h*u, h >= 1} and V = {k*v, k >= 1}. Then A187393(n) is the position of n*u in the ordered union of U and V, and A187394 is the position of n*v. - Clark Kimberling, Oct 21 2014

Links

• N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence)

Crossrefs

Cf. A187394.

A bisection of A001952.

Programs

Magma

[Floor (n*(4+Sqrt(8))): n in [1..100]]; // Vincenzo Librandi, Oct 23 2014

Mathematica

r=4+8^(1/2); s=4-8^(1/2);
Table[Floor[r*n],{n,1,80}]  (* A187393 *)
Table[Floor[s*n],{n,1,80}]  (* A187394 *)

Python

from sympy import integer_nthroot
def A187393(n): return 4*n+integer_nthroot(8*n**2,2)[0] # Chai Wah Wu, Mar 16 2021

Formula

a(n) = floor(r*n), where r = 4 + sqrt(8).