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A004483 Tersum n + 2. 3
2, 0, 1, 5, 3, 4, 8, 6, 7, 11, 9, 10, 14, 12, 13, 17, 15, 16, 20, 18, 19, 23, 21, 22, 26, 24, 25, 29, 27, 28, 32, 30, 31, 35, 33, 34, 38, 36, 37, 41, 39, 40, 44, 42, 43, 47, 45, 46, 50, 48, 49, 53, 51, 52, 56, 54, 55, 59, 57, 58, 62, 60, 61, 65, 63, 64, 68, 66, 67 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..68.

A. Dress, A. Flammenkamp and N. 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[ n/3 ] + ((n+2) mod 3).

a(n)= -2 + Sum_{k=0..n}{1/3*(-2*(k mod 3)-2*((k+1) mod 3)+7*((k+2) mod 3)}, with n>=0 - Paolo P. Lava, Oct 26 2007

a(n) = n + 2*cos(2*n*Pi/3). - Wesley Ivan Hurt, Sep 27 2017

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.- R. J. Mathar, Dec 14 2017

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

This sequence is row 2 of table A004481.

Second column of triangle in A296339.

Sequence in context: A163940 A112340 A037186 * A197808 A085650 A201910

Adjacent sequences:  A004480 A004481 A004482 * A004484 A004485 A004486

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Edited by N. J. A. Sloane at the suggestion of Philippe Deléham, Nov 20 2007

STATUS

approved

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Last modified November 20 02:57 EST 2018. Contains 317371 sequences. (Running on oeis4.)