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A003512
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A Beatty sequence: floor(n*(sqrt(3) + 2)).
(Formerly M2622)
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11
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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)
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OFFSET
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1,1
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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For n >= 0, a(n) = 2n + largest integer m such that m^2 <= 3*n^2. - Chai Wah Wu, Oct 08 2016
For n > 0, a(n) = 4*floor(n*(sqrt(3)-1)) + 3*floor(n*(2-sqrt(3))) + 3;
(End)
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MAPLE
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Digits := 60: A003512 := proc(n) trunc( evalf( n*(sqrt(3)+2) )); end;
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MATHEMATICA
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PROG
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(Python)
from gmpy2 import isqrt
return 2*n + int(isqrt(3*n**2)) # Chai Wah Wu, Oct 08 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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