A004482 Tersum n + 1 (answer recorded in base 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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• base

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.
• Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Crossrefs

This sequence is row 1 of table A004481.

a(n) = A061347(n+1) + n.

Third column of triangle A296339.

Programs

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 *)

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

Extensions

More terms from Erich Friedman