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!)
 A001953 a(n) = floor((n + 1/2) * sqrt(2)). (Formerly M0543 N0193) 5
 0, 2, 3, 4, 6, 7, 9, 10, 12, 13, 14, 16, 17, 19, 20, 21, 23, 24, 26, 27, 28, 30, 31, 33, 34, 36, 37, 38, 40, 41, 43, 44, 45, 47, 48, 50, 51, 53, 54, 55, 57, 58, 60, 61, 62, 64, 65, 67, 68, 70, 71, 72, 74, 75, 77, 78, 79, 81, 82, 84, 85, 86, 88, 89, 91, 92, 94, 95 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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's, 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. N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence) FORMULA From Ralf Steiner, Oct 23 2019: (Start) a(n) = floor(2*sqrt(A000217(n))). a(n) = A136119(n + 1) - 1. a(n + 1) - a(n) is in {1,2}. a(n + 3) - a(n) is in {4,5}. (End) MAPLE seq( floor((2*n+1)/sqrt(2)), n=0..100); # G. C. Greubel, Nov 14 2019 MATHEMATICA Table[Floor[(n + 1/2) Sqrt[2]], {n, 0, 100}] (* T. D. Noe, Aug 17 2012 *) PROG (PARI) a(n)=floor((n+1/2)*sqrt(2)) (PARI) a(n)={sqrtint(2*n*(n+1))} \\ Andrew Howroyd, Oct 24 2019 (MAGMA) [Floor((2*n+1)/Sqrt(2)): n in [0..100]]; // G. C. Greubel, Nov 14 2019 (Sage) [floor((2*n+1)/sqrt(2)) for n in (0..100)] # G. C. Greubel, Nov 14 2019 CROSSREFS Complement of A001954. Cf. A000217 (T), A136119, A001108. Sequence in context: A214857 A175320 A325597 * A230748 A078607 A292043 Adjacent sequences:  A001950 A001951 A001952 * A001954 A001955 A001956 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 16 08:07 EDT 2021. Contains 343940 sequences. (Running on oeis4.)