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 A187393 Floor(r*n), where r = 4 + sqrt(8); complement of A187394. 2
 6, 13, 20, 27, 34, 40, 47, 54, 61, 68, 75, 81, 88, 95, 102, 109, 116, 122, 129, 136, 143, 150, 157, 163, 170, 177, 184, 191, 198, 204, 211, 218, 225, 232, 238, 245, 252, 259, 266, 273, 279, 286, 293, 300, 307, 314, 320, 327, 334, 341, 348, 355, 361, 368, 375, 382, 389, 396, 402, 409, 416, 423, 430, 437, 443, 450, 457, 464, 471, 477 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A187393 and A187394 are the Beatty sequences for 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 FORMULA a(n) = floor(r*n), where r = 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 [1..100]]; // Vincenzo Librandi, Oct 23 2014 CROSSREFS Cf. A187394. Sequence in context: A189523 A003329 A048929 * A043417 A031485 A004919 Adjacent sequences:  A187390 A187391 A187392 * A187394 A187395 A187396 KEYWORD nonn AUTHOR Clark Kimberling, Mar 09 2011 STATUS approved

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Last modified February 28 22:24 EST 2020. Contains 332335 sequences. (Running on oeis4.)