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
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Michael Somos, Apr 26 2000.
STATUS
approved