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A004202 Skip 1, take 1, skip 2, take 2, skip 3, take 3, etc. 12
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; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
a(n) are the numbers satisfying m < sqrt(a(n)) < m + 0.5 for some integer m. - Floor van Lamoen, 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
Positions of record values in A256188 that are greater than 1: A014132(n) = A256188(a(n)). - Reinhard Zumkeller, Mar 26 2015
LINKS
FORMULA
a(n) = n + A000217(A002024(n)). - M. F. Hasler, Feb 13 2011
T(n, k) = n^2 + k, for n>=1, k>=1 as a triangular array. a(n) = n + A127739(n). - Michael Somos, May 03 2019
EXAMPLE
Interpretation as Wythoff sequence (from Clark Kimberling):
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.
From Michael Somos, May 03 2019: (Start)
As a triangular array
2;
5, 6;
10, 11, 12;
17, 18, 19, 20;
(End)
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]
a[ n_] := If[ n < 1, 0, With[{m = Round@Sqrt[2 n]}, n + m (m + 1)/2]]; (* Michael Somos, May 03 2019 *)
Take[#, (-Length[#])/2]&/@Module[{nn=20}, TakeList[Range[ nn+nn^2], 2*Range[ nn]]]//Flatten (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 13 2019 *)
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
(PARI) {a(n) = my(m); if( n<1, 0, m=round(sqrt(2*n)); n + m*(m+1)/2)}; /* Michael Somos, May 03 2019 */
CROSSREFS
Sequence in context: A244731 A307562 A109150 * A013647 A255068 A183987
KEYWORD
nonn,tabl
AUTHOR
Alexander Stasinski
STATUS
approved

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Last modified May 29 11:28 EDT 2024. Contains 372940 sequences. (Running on oeis4.)