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 A003512 A Beatty sequence: floor(n*(sqrt(3) + 2)). (Formerly M2622) 11
 3, 7, 11, 14, 18, 22, 26, 29, 33, 37, 41, 44, 48, 52, 55, 59, 63, 67, 70, 74, 78, 82, 85, 89, 93, 97, 100, 104, 108, 111, 115, 119, 123, 126, 130, 134, 138, 141, 145, 149, 153, 156, 160, 164, 167, 171, 175, 179, 182, 186 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10000 Aviezri S. Fraenkel, Jonathan Levitt, Michael Shimshoni, Characterization of the set of values f(n)=[n alpha], n=1,2,..., Discrete Math. 2 (1972), no.4, 335-345. Eric Weisstein's World of Mathematics, Beatty Sequence. FORMULA a(n) = floor(n*(sqrt(3)+2)). - Michel Marcus, Jan 05 2015 For n >= 0, a(n) = 2n + largest integer m such that m^2 <= 3*n^2. - Chai Wah Wu, Oct 08 2016 From Miko Labalan, Dec 03 2016: (Start) For n > 0, a(n) = 4*floor(n*(sqrt(3)-1)) + 3*floor(n*(2-sqrt(3))) + 3; a(0) = 0, a(n) = a(n - 1) + A182778(n) - A182778(n - 1) - 1. (End) MAPLE Digits := 60: A003512 := proc(n) trunc( evalf( n*(sqrt(3)+2) )); end; MATHEMATICA Table[Floor[n (Sqrt@ 3 + 2)], {n, 50}] (* Michael De Vlieger, Oct 08 2016 *) PROG (Python) from gmpy2 import isqrt def A003512(n):     return 2*n + int(isqrt(3*n**2))  # Chai Wah Wu, Oct 08 2016 CROSSREFS Cf. A003511 (complement), A019973 (sqrt(3)+2). Sequence in context: A260484 A000572 A059568 * A246170 A190694 A310206 Adjacent sequences:  A003509 A003510 A003511 * A003513 A003514 A003515 KEYWORD nonn AUTHOR STATUS approved

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Last modified February 25 08:48 EST 2020. Contains 332221 sequences. (Running on oeis4.)