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A004202
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Skip 1, take 1, skip 2, take 2, skip 3, take 3, etc.
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8
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2, 5, 6, 10, 11, 12, 17, 18, 19, 20, 26, 27, 28, 29, 30, 37, 38, 39, 40, 41, 42, 50, 51, 52, 53, 54, 55, 56, 65, 66, 67, 68, 69, 70, 71, 72, 82, 83, 84, 85, 86, 87, 88, 89, 90, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(n) are the numbers satisfying m < sqrt(a(n)) < m + 0.5 for some integer m. - Floor van Lamoen (fvlamoen(AT)hotmail.com), Jul 24 2001
a(A000217(n)) = A002378(n). [Reinhard Zumkeller, Feb 12 2011]
Complement of A004201. Upper s(n)-Wythoff sequence (as defined in A184117), for s(n)=A002024(n)=floor[1/2+sqrt(2n)]. I.e., A004202(n) = A002024(n) + A004201(n), with A004201(1)=1 and for n>1, A004201(n) = least positive integer not yet in (A004201(1..n-1) union A004202(1..n-1)). - M. F. Hasler (following observations from R. J. Mathar), Feb 13 2011
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FORMULA
| a(n) = n + A000217(A002024(n)). - M. F. Hasler, Feb 13 2011
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EXAMPLE
| Interpretation as Wythoff sequence (from Clark Kimberling (ck6(AT)evansville.edu)):
s = (1,2,2,3,3,3,4,4,4,4...) = A002024 (n n's);
a = (1,3,4,7,8,9,13,14,...) = A004201 = least number > 0 not yet in a or b;
b = (2,5,6,10,11,12,17,18,...) = A004202 = a+s.
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MATHEMATICA
| a = Table[n, {n, 1, 210} ]; b = {}; Do[a = Drop[a, {1, n} ]; b = Append[b, Take[a, {1, n} ]]; a = Drop[a, {1, n} ], {n, 1, 14} ]; Flatten[b]
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PROG
| (Haskell)
a004202 n = a004202_list !! (n-1)
a004202_list = skipTake 1 [1..] where
skipTake k xs = take k (drop k xs) ++ skipTake (k + 1) (drop (2*k) xs
-- Reinhard Zumkeller, Feb 12 2011
(PARI) A004202(n) = n+0+(n=(sqrtint(8*n-7)+1)\2)*(n+1)\2 \\ - M. F. Hasler, Feb 13 2011
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CROSSREFS
| Cf. A004201, A007606, A064801.
Sequence in context: A184418 A112967 A109150 * A013647 A183987 A187840
Adjacent sequences: A004199 A004200 A004201 * A004203 A004204 A004205
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KEYWORD
| nonn
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AUTHOR
| Alexander Stasinski
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