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A004201
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Accept one, reject one, accept two, reject two, ...
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13
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1, 3, 4, 7, 8, 9, 13, 14, 15, 16, 21, 22, 23, 24, 25, 31, 32, 33, 34, 35, 36, 43, 44, 45, 46, 47, 48, 49, 57, 58, 59, 60, 61, 62, 63, 64, 73, 74, 75, 76, 77, 78, 79, 80, 81, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 133, 134, 135
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OFFSET
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1,2
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COMMENTS
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a(n) are the numbers satisfying m - 0.5 < sqrt(a(n)) <= m for some positive integer m. - Floor van Lamoen, Jul 24 2001
Lower s(n)-Wythoff sequence (as defined in A184117) associated to s(n) = A002024(n) = floor(1/2+sqrt(2n)), with complement (upper s(n)-Wythoff sequence) in A004202.
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LINKS
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FORMULA
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a(n) = n + t(t+1)/2, where t = floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Dec 13 2012
a(n) = (2*n - r + r^2)/2, where r = round(sqrt(2*n)). - Wesley Ivan Hurt, Sep 20 2021
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MATHEMATICA
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f[x_]:=Module[{c=1-x+x^2}, Range[c, c+x-1]]; Flatten[Array[f, 20]] (* Harvey P. Dale, Jul 31 2012 *)
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PROG
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(Haskell)
a004201 n = a004201_list !! (n-1)
a004201_list = f 1 [1..] where
f k xs = us ++ f (k + 1) (drop (k) vs) where (us, vs) = splitAt k xs
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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Alexander Stasinski
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STATUS
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approved
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