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%I #43 Sep 26 2021 11:04:47
%S 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,
%T 47,48,49,57,58,59,60,61,62,63,64,73,74,75,76,77,78,79,80,81,91,92,93,
%U 94,95,96,97,98,99,100,111,112,113,114,115,116,117,118,119,120,121,133,134,135
%N Accept one, reject one, accept two, reject two, ...
%C a(n) are the numbers satisfying m - 0.5 < sqrt(a(n)) <= m for some positive integer m. - _Floor van Lamoen_, Jul 24 2001
%C 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.
%H Harvey P. Dale, <a href="/A004201/b004201.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A061885(n-1)+1. - _Franklin T. Adams-Watters_, Jul 05 2009
%F a(n+1) - a(n) = A130296(n+1). - _Reinhard Zumkeller_, Jul 16 2008
%F a(A000217(n)) = n^2. - _Reinhard Zumkeller_, Feb 12 2011
%F a(n) = A004202(n)-A002024(n). - _M. F. Hasler_, Feb 13 2011
%F a(n) = n+A000217(A003056(n-1)) = n+A000217(A002024(n)-1). - _M. F. Hasler_, Feb 13 2011
%F a(n) = n + t(t+1)/2, where t = floor((-1+sqrt(8*n-7))/2). - _Boris Putievskiy_, Dec 13 2012
%F a(n) = (2*n - r + r^2)/2, where r = round(sqrt(2*n)). - _Wesley Ivan Hurt_, Sep 20 2021
%t f[x_]:=Module[{c=1-x+x^2},Range[c,c+x-1]]; Flatten[Array[f,20]] (* _Harvey P. Dale_, Jul 31 2012 *)
%o (Haskell)
%o a004201 n = a004201_list !! (n-1)
%o a004201_list = f 1 [1..] where
%o f k xs = us ++ f (k + 1) (drop (k) vs) where (us, vs) = splitAt k xs
%o -- _Reinhard Zumkeller_, Jun 20 2015, Feb 12 2011
%o (PARI) A004201(n)=n+(n=(sqrtint(8*n-7)+1)\2)*(n-1)\2 \\ _M. F. Hasler_, Feb 13 2011
%Y Cf. A002024, A004202, A007606.
%K nonn,nice
%O 1,2
%A Alexander Stasinski
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