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A004482 Tersum n + 1 (answer recorded in base 10). 10
1, 2, 0, 4, 5, 3, 7, 8, 6, 10, 11, 9, 13, 14, 12, 16, 17, 15, 19, 20, 18, 22, 23, 21, 25, 26, 24, 28, 29, 27, 31, 32, 30, 34, 35, 33, 37, 38, 36, 40, 41, 39, 43, 44, 42, 46, 47, 45, 49, 50, 48, 52, 53, 51, 55, 56, 54, 58, 59, 57, 61, 62 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
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.
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
F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, Queens in exile: non-attacking queens on infinite chess boards, Electronic J. Combin., 27:1 (2020), Article P1.52.
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).
Gabriel Nivasch, More on the Sprague-Grundy function for Wythoff’s game, pages 377-410 in "Games of No Chance 3, MSRI Publications Volume 56, 2009. See Table 1.
FORMULA
Periodic with period 3 and saltus 3: a(n) = 3*floor(n/3) + ((n+1) mod 3).
a(n) = n - 2*cos(2*(n+1)*Pi/3). - Wesley Ivan Hurt, Sep 29 2017
Sum_{n>=3} (-1)^(n+1)/a(n) = 1/2 - log(2)/3. - Amiram Eldar, Aug 21 2023
MATHEMATICA
LinearRecurrence[{1, 0, 1, -1}, {1, 2, 0, 4}, 70] (* or *) Table[3*Floor[n/3]+ Mod[ n+1, 3], {n, 0, 70}] (* Harvey P. Dale, Nov 29 2014 *)
CROSSREFS
This sequence is row 1 of table A004481.
a(n) = A061347(n+1) + n.
Third column of triangle A296339.
Sequence in context: A335118 A201837 A326052 * A329233 A111677 A326186
KEYWORD
nonn,easy,base
AUTHOR
EXTENSIONS
More terms from Erich Friedman
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)