|
|
|
|
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
|
|
|
FORMULA
|
Periodic with period and saltus 3: a(n) = 3*floor(n/3) + ((n+2) mod 3).
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
|
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.
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|