A187338 a(n) = 3*n + floor(sqrt(2)*n), complement of A187328.

4, 8, 13, 17, 22, 26, 30, 35, 39, 44, 48, 52, 57, 61, 66, 70, 75, 79, 83, 88, 92, 97, 101, 105, 110, 114, 119, 123, 128, 132, 136, 141, 145, 150, 154, 158, 163, 167, 172, 176, 180, 185, 189, 194, 198, 203, 207, 211, 216, 220, 225, 229, 233, 238, 242, 247, 251, 256, 260, 264, 269, 273, 278, 282, 286, 291, 295, 300

Offset

1,1

Comments

A187338 and A187328 are a pair of Beatty sequences. The following three sequences partition the natural numbers:

A190329: a(n)=n+[n*sqrt(2)]+[n/sqrt(2)].

A190330: b(n)=n+[n/sqrt(2)]+[n/2)].

A187338: c(n)=3n+[n*sqrt(2)].

Links

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

Formula

a(n) = 3*n + floor(sqrt(2)*n) = 3n+A001951(n).

Mathematica

Table[Floor[(3+2^(1/2))n], {n, 1, 120}]
With[{c=3+Sqrt[2]}, Floor[c*Range[70]]] (* Harvey P. Dale, Aug 15 2013 *)

Prog

(PARI) for(n=1, 70, print1(3*n + floor(sqrt(2)*n), ", ")) \\ G. C. Greubel, Jan 29 2018
(Magma) [3*n + Floor(Sqrt(2)*n): n in [1..70]]; // G. C. Greubel, Jan 29 2018
(Python)
from sympy import integer_nthroot
def A187338(n): return 3*n+integer_nthroot(2*n**2, 2)[0] # Chai Wah Wu, Mar 17 2021

Crossrefs

Cf. A187328.

Sequence in context: A311922 A311923 A311924 * A311925 A311926 A311927

Adjacent sequences: A187335 A187336 A187337 * A187339 A187340 A187341

Keyword

nonn

Author

Clark Kimberling, Mar 08 2011

Status

approved