The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A001954 Wythoff game. (Formerly M3774 N1539) 5
 1, 5, 8, 11, 15, 18, 22, 25, 29, 32, 35, 39, 42, 46, 49, 52, 56, 59, 63, 66, 69, 73, 76, 80, 83, 87, 90, 93, 97, 100, 104, 107, 110, 114, 117, 121, 124, 128, 131, 134, 138, 141, 145, 148, 151, 155, 158, 162, 165, 169, 172, 175, 179, 182, 186, 189, 192, 196, 199 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Winning positions in the 2-Wythoff game, the u-pile in Connell's nomenclature; v-pile numbers in A001953. Let s(n) = zeta(3) - Sum_{k=1..n} 1/k^3.  Conjecture:  for n >=1, s(a(n)) < 1/n^2 < s(a(n)-1), and the difference sequence of A049473 consists solely of 0's and 1, in positions given by the nonhomogeneous Beatty sequences A001954 and A001953, respectively. - Clark Kimberling, Oct 05 2014 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n = 0..10000 Ian G. Connell, A generalization of Wythoff's game, Canad. Math. Bull. 2 (1959) 181-190 J. N. Cooper and A. W. N. Riasanovsky, On the Reciprocal of the Binary Generating Function for the Sum of Divisors, 2012; J. Int. Seq. 16 (2013) #13.1.8 N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence) FORMULA a(n) = floor((n+1/2)*(2+sqrt(2))). a(n + 1) - a(n) is either 3 or 4. Note the comment regarding some intervals in the complement (A001953). - Ralf Steiner, Oct 27 2019 MAPLE seq( floor((2+sqrt(2))*(2*n+1)/2), n=0..70); # G. C. Greubel, Dec 20 2019 MATHEMATICA Table[Floor[(n + 1/2) (2 + Sqrt)], {n, 0, 100}] (* T. D. Noe, Aug 17 2012 *) Complement[Range, Table[Floor[Sqrt[2*n*(n + 1)]], {n, 0, 300}]] (* Ralf Steiner, Oct 27 2019 *) PROG (PARI) a(n)=floor((n+1/2)*(2+sqrt(2))) (MAGMA) [Floor((2+Sqrt(2))*(2*n+1)/2): n in [0..70]]; // G. C. Greubel, Dec 20 2019 (Sage) [floor((2+sqrt(2))*(2*n+1)/2) for n in (0..70)] # G. C. Greubel, Dec 20 2019 CROSSREFS Complement of A001953. Bisection of A003152. Sequence in context: A186238 A314389 A118520 * A006620 A176628 A314390 Adjacent sequences:  A001951 A001952 A001953 * A001955 A001956 A001957 KEYWORD nonn AUTHOR EXTENSIONS More terms from Michael Somos, Apr 26 2000 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 14 16:48 EDT 2021. Contains 343898 sequences. (Running on oeis4.)