A277644 Beatty sequence for sqrt(6)/2.

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 15, 17, 18, 19, 20, 22, 23, 24, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 39, 40, 41, 42, 44, 45, 46, 47, 48, 50, 51, 52, 53, 55, 56, 57, 58, 60, 61, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 74, 75, 77, 78, 79, 80, 82, 83, 84, 85, 86

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(5)=6 because the quotient of 3*5^2 by 2 is 37 which lies between 6^2 and 7^2.
		

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, A032528, A115754, A277515. Complement of A277645.

Programs

Magma

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

Mathematica

Floor[Range[100]*Sqrt[3/2]] (* Paolo Xausa, Jul 11 2024 *)

PARI

a(n)=sqrtint(3*n^2\2) \\ Charles R Greathouse IV, Jul 11 2024

Formula

a(n) = floor(n*sqrt(6)/2).

a(n) = A000196(A032528(n)).