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A004201
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Accept one, reject one, accept two, reject two, ...
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12
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) are the numbers satisfying m - 0.5 < sqrt(a(n)) <= m for some positive integer m. - Floor van Lamoen (fvlamoen(AT)hotmail.com), 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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FORMULA
| a(n) = A061885(n-1)+1. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jul 05 2009]
a(n+1) - a(n) = A130296(n+1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 16 2008
a(A000217(n)) = n^2. [Reinhard Zumkeller, Feb 12 2011]
a(n) = A004202(n)-A002024(n). - M. F. Hasler, Feb 13 2011
a(n) = n+A000217(A003056(n-1)) = n+A000217(A002024(n)-1). - M. F. Hasler, Feb 13 2011
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PROG
| (Haskell)
a004201 n = a004201_list !! (n-1)
a004201_list = takeSkip 1 [1..] where
takeSkip k xs = take k xs ++ takeSkip (k + 1) (drop (2*k) xs)
-- Reinhard Zumkeller, Feb 12 2011
(PARI) A004201(n)=n+(n=(sqrtint(8*n-7)+1)\2)*(n-1)\2 \\ - M. F. Hasler, Feb 13 2011
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CROSSREFS
| Cf. A004202, A007606.
Sequence in context: A175054 A154366 A100452 * A109054 A129142 A075752
Adjacent sequences: A004198 A004199 A004200 * A004202 A004203 A004204
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KEYWORD
| nonn,nice
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AUTHOR
| Alexander Stasinski
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