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A004202 Skip 1, take 1, skip 2, take 2, skip 3, take 3, etc. 11
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; 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

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = n + A000217(A002024(n)). - M. F. Hasler, Feb 13 2011

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.

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]

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

CROSSREFS

Cf. A004201, A007606, A064801.

Cf. A014132, A256188.

Sequence in context: A112967 A244731 A109150 * A013647 A255068 A183987

Adjacent sequences:  A004199 A004200 A004201 * A004203 A004204 A004205

KEYWORD

nonn

AUTHOR

Alexander Stasinski

STATUS

approved

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Last modified March 24 15:46 EDT 2017. Contains 283991 sequences.