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A187394 Floor(s*n), where s = 4 - sqrt(8); complement of A187393. 2
1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 96, 97, 98, 99, 100, 101, 103, 104, 105, 106, 107, 108, 110, 111, 112, 113, 114, 115, 117 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A187393 and A187394 are the Beatty sequences based on r = 4 + sqrt(8) and s = 4 - sqrt(8); 1/r + 1/s = 1.

Let u = 1 + sqrt(2) and v = -1 + sqrt(2).  Let U = {h*u, h >= 1} and V = {k*v, k >= 1}.  Then A187393(n) is the position of n*u in the ordered union of U and V, and A187394 is the position of n*v.  - Clark Kimberling, Oct 21 2014

LINKS

Table of n, a(n) for n=1..100.

FORMULA

a(n) = floor(s*n), where s = 4 - sqrt(8).

MATHEMATICA

r=4+8^(1/2); s=4-8^(1/2);

Table[Floor[r*n], {n, 1, 80}]  (* A187393 *)

Table[Floor[s*n], {n, 1, 80}]  (* A187394 *)

PROG

(MAGMA) [Floor (n*(4-Sqrt(8))): n in [0..100]]; // Vincenzo Librandi, Oct 23 2014

CROSSREFS

Cf. A187393.

Sequence in context: A047368 A020657 A037470 * A057907 A109234 A335137

Adjacent sequences:  A187391 A187392 A187393 * A187395 A187396 A187397

KEYWORD

nonn

AUTHOR

Clark Kimberling, Mar 09 2011

STATUS

approved

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Last modified May 29 20:42 EDT 2020. Contains 334710 sequences. (Running on oeis4.)