A187386 a(n) = floor(s*n), where s=1+sqrt(3)-sqrt(2); complement of A187385.

1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 25, 26, 27, 28, 30, 31, 32, 34, 35, 36, 38, 39, 40, 42, 43, 44, 46, 47, 48, 50, 51, 52, 54, 55, 56, 57, 59, 60, 61, 63, 64, 65, 67, 68, 69, 71, 72, 73, 75, 76, 77, 79, 80, 81, 83, 84, 85, 86, 88, 89, 90, 92, 93, 94, 96, 97, 98, 100, 101, 102, 104, 105

Offset

1,2

Comments

A187385 and A187386 are the Beatty sequences based on r=1+sqrt(3)+sqrt(2) and s=1+sqrt(3)-sqrt(2); 1/r+1/s=1.

Links

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

Index entries for sequences related to Beatty sequences

Formula

a(n) = floor(s*n), where s=1+sqrt(3)-sqrt(2).

Mathematica

k=3; r=1+k^(1/2)+(k-1)^(1/2); s=1+k^(1/2)-(k-1)^(1/2);
Table[Floor[r*n], {n, 1, 80}]  (* A187385 *)
Table[Floor[s*n], {n, 1, 80}]  (* A187386 *)

Prog

(PARI) vector(120, n, floor(n*(sqrt(3) - sqrt(2) + 1))) \\ G. C. Greubel, Aug 19 2018
(Magma) [Floor(n*(Sqrt(3) - Sqrt(2) +1)): n in [1..120]]; // G. C. Greubel, Aug 19 2018

Crossrefs

Cf. A187385.

Sequence in context: A329990 A109237 A164087 * A059531 A039053 A352675

Adjacent sequences: A187383 A187384 A187385 * A187387 A187388 A187389

Keyword

nonn

Author

Clark Kimberling, Mar 09 2011

Status

approved