A194152 Beatty sequence for 5+2*sqrt(5); complement of A194151.

9, 18, 28, 37, 47, 56, 66, 75, 85, 94, 104, 113, 123, 132, 142, 151, 161, 170, 179, 189, 198, 208, 217, 227, 236, 246, 255, 265, 274, 284, 293, 303, 312, 322, 331, 340, 350, 359, 369, 378, 388, 397, 407, 416, 426, 435, 445, 454, 464, 473, 483, 492, 502

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Formula

a(n) = 5*n + A022839(2*n). - R. J. Mathar, Aug 25 2011

a(n) = floor(n*(5+2*sqrt(5))). - Vincenzo Librandi, Oct 25 2011

Mathematica

r=Sqrt[5]/2;
c[k_]:=Floor[k*r];
Table[c[k], {k, 1, 90}] (* A194151 *)
s=5+2*Sqrt[5];
d[k_]:=Floor[k*s];
Table[d[k], {k, 1, 90}] (* A194152 *)

Prog

(Magma) [Floor(n*(5+2*Sqrt(5))): n in [1..80]]; // Vincenzo Librandi, Oct 25 2011
(Python)
from sympy import integer_nthroot
def A194152(n): return 5*n+integer_nthroot(20*n**2, 2)[0] # Chai Wah Wu, Mar 16 2021

Crossrefs

Cf. A022839, A194151.

Sequence in context: A071121 A157644 A107223 * A044433 A161570 A140089

Adjacent sequences: A194149 A194150 A194151 * A194153 A194154 A194155

Keyword

nonn

Author

Clark Kimberling, Aug 17 2011

Status

approved