A194145 Beatty sequence for -1+sqrt(6), a(n) = floor(n*(-1+sqrt(6))); complement of A194146.

1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 15, 17, 18, 20, 21, 23, 24, 26, 27, 28, 30, 31, 33, 34, 36, 37, 39, 40, 42, 43, 44, 46, 47, 49, 50, 52, 53, 55, 56, 57, 59, 60, 62, 63, 65, 66, 68, 69, 71, 72, 73, 75, 76, 78, 79, 81, 82, 84, 85, 86, 88, 89, 91, 92, 94, 95, 97, 98

Offset

1,2

Comments

Beatty sequence for 1.449489742783...

Beatty sequences occur in complementary pairs; the complement of this is the Beatty sequence for 2+(1/2)*sqrt(6), at A194146.

Links

Table of n, a(n) for n=1..68.

Index entries for sequences related to Beatty sequences

Mathematica

r=-1+Sqrt[6];
c[k_]:=Floor[k*r];
Table[c[k], {k, 1, 90}] (* A194145 *)
s=r/(r-1);
d[k_]:=Floor[k*s];
Table[d[k], {k, 1, 90}] (* A194146 *)

Prog

(Python)
from sympy import integer_nthroot
def A194145(n): return integer_nthroot(6*n**2, 2)[0]-n # Chai Wah Wu, Mar 16 2021

Crossrefs

Cf. A194146.

Sequence in context: A072633 A037087 A320829 * A330116 A189784 A062005

Adjacent sequences: A194142 A194143 A194144 * A194146 A194147 A194148

Keyword

nonn

Author

Clark Kimberling, Aug 17 2011

Status

approved