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A004201 Accept one, reject one, accept two, reject two, ... 12
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; text; internal format)
OFFSET

1,2

COMMENTS

a(n) are the numbers satisfying m - 0.5 < sqrt(a(n)) <= m for some positive integer m. - Floor van Lamoen, 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.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A061885(n-1)+1. - Franklin T. Adams-Watters, Jul 05 2009

a(n+1) - a(n) = A130296(n+1). - Reinhard Zumkeller, 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

a(n) = n + t(t+1)/2, where t = floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Dec 13 2012

MATHEMATICA

f[x_]:=Module[{c=1-x+x^2}, Range[c, c+x-1]]; Flatten[Array[f, 20]] (* Harvey P. Dale, Jul 31 2012 *)

PROG

(Haskell)

a004201 n = a004201_list !! (n-1)

a004201_list = f 1 [1..] where

   f k xs = us ++ f (k + 1) (drop (k) vs) where (us, vs) = splitAt k xs

-- Reinhard Zumkeller, Jun 20 2015, Feb 12 2011

(PARI) A004201(n)=n+(n=(sqrtint(8*n-7)+1)\2)*(n-1)\2  \\ M. F. Hasler, Feb 13 2011

CROSSREFS

Cf. A004202, A007606.

Sequence in context: A154366 A226227 A100452 * A109054 A129142 A075752

Adjacent sequences:  A004198 A004199 A004200 * A004202 A004203 A004204

KEYWORD

nonn,nice,changed

AUTHOR

Alexander Stasinski

STATUS

approved

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Last modified June 27 14:52 EDT 2017. Contains 288790 sequences.