OFFSET
0,1
COMMENTS
Tersum m + n: write m and n in base 3 and add mod 3 with no carries; e.g., 5 + 8 = "21" + "22" = "10" = 1.
Also Sprague-Grundy values for game of Wyt Queens.
REFERENCES
E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 76.
LINKS
Andreas Dress, Achim Flammenkamp, and Norbert Pink, Additive periodicity of the Sprague-Grundy function of certain Nim games, Adv. Appl. Math., 22, p. 249-270 (1999).
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
FORMULA
Periodic with period and saltus 3: a(n) = 3*floor(n/3) + ((n+2) mod 3).
a(n) = n + 2*cos(2*n*Pi/3). - Wesley Ivan Hurt, Sep 27 2017
From R. J. Mathar, Dec 14 2017: (Start)
G.f.: ( 2+x^2+2*x^3-2*x ) / ( (1+x+x^2)*(x-1)^2 ).
a(n) = n + A099837(n) if n > 0. (End)
Sum_{n>=2} (-1)^n/a(n) = 2*Pi/(3*sqrt(3)) + log(2)/3 - 1/2. - Amiram Eldar, Aug 21 2023
MATHEMATICA
a[n_] := If[Divisible[n, 3], n+2, n-1]; Table[a[n], {n, 0, 70}] (* Jean-François Alcover, Oct 25 2013 *)
LinearRecurrence[{1, 0, 1, -1}, {2, 0, 1, 5}, 70] (* Harvey P. Dale, Feb 07 2018 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane at the suggestion of Philippe Deléham, Nov 20 2007
STATUS
approved