A277645 Beatty sequence for 3+sqrt(6).

5, 10, 16, 21, 27, 32, 38, 43, 49, 54, 59, 65, 70, 76, 81, 87, 92, 98, 103, 108, 114, 119, 125, 130, 136, 141, 147, 152, 158, 163, 168, 174, 179, 185, 190, 196, 201, 207, 212, 217, 223, 228, 234, 239, 245, 250, 256, 261, 267, 272, 277, 283, 288, 294, 299, 305

Offset: 1

Author

Jason Kimberley, Oct 26 2016

Keywords

• nonn
• easy

Comments

Eggleton et al. show that k is in this sequence if and only if A277515(k) > 3.

Examples

			a(4) = 3*4 + 9 because 9^2 = 81 < 6*4^2 = 96 < 100 = 10^2.
		

References

• R. B. Eggleton, J. S. Kimberley, and J. A. MacDougall, Square-free rank of integers, submitted.

Links

• Jason Kimberley, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Beatty Sequence.
• Index entries for sequences related to Beatty sequences.

Crossrefs

Cf. A000196, A008585, A010464, A033581, A277515.

Complement of A277644.

Programs

Magma

[3*n+Isqrt(6*n^2): n in [1..60]];

Mathematica

Floor[Range[100]*(3 + Sqrt[6])] (* Paolo Xausa, Jul 11 2024 *)

Formula

a(n) = floor(n*(3+sqrt(6))).

a(n) = 3*n + A000196(A033581(n)).

a(n) = A008585(n) + A000196(A033581(n)).