OFFSET
0,1
COMMENTS
Start with 3. Then repeat the cycle: subtract 3, add 5. The odd-indexed terms give the odd numbers, beginning with 3. The even-indexed terms give the even numbers, beginning with 0. In the infinite sequence, every positive integer except 1 is listed.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
a(n) = 2*n-a(n-1)+1 (with a(0)=3). - Vincenzo Librandi, Dec 02 2010
a(n) = 1 + n + 2*(-1)^n. - R. J. Mathar, Dec 02 2010
From Colin Barker, Nov 05 2015: (Start)
a(n) = a(n-1) + a(n-2) - a(n-3) for n>2.
G.f.: (2*x^2-3*x+3) / ((x-1)^2*(x+1)). (End)
Sum_{n>=2} (-1)^(n+1)/a(n) = 4/3 - log(2). - Amiram Eldar, Sep 10 2023
EXAMPLE
For n = 3, Nimsum(3 + 4 + 5) = 2, as shown: 011 XOR 100 XOR 101 010.
MAPLE
read("transforms") ; A165754 := proc(n) nimsum(nimsum(n, n+1), n+2) ; end: seq(A165754(n), n=0..120) ; # R. J. Mathar, Sep 28 2009
MATHEMATICA
Flatten[NestList[{Last[#]+5, Last[#]+2}&, {3, 0}, 40]] (* Harvey P. Dale, Dec 04 2011 *)
PROG
(Python)
n = 0
while n < 100:
print(n^(n+1)^(n+2), end=', ')
n += 1
(PARI) Vec((2*x^2-3*x+3)/((x-1)^2*(x+1)) + O(x^100)) \\ Colin Barker, Nov 05 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mick Purcell (mickpurcell(AT)gmail.com), Sep 26 2009
EXTENSIONS
Extended by R. J. Mathar, Sep 28 2009
STATUS
approved