A187393 - OEIS

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

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OFFSET

1,1

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

Table of n, a(n) for n=1..70.

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

FORMULA

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

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 *)

PROG

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

(Python)