A165754 a(n) = nimsum(n+(n+1)+(n+2)).

3, 0, 5, 2, 7, 4, 9, 6, 11, 8, 13, 10, 15, 12, 17, 14, 19, 16, 21, 18, 23, 20, 25, 22, 27, 24, 29, 26, 31, 28, 33, 30, 35, 32, 37, 34, 39, 36, 41, 38, 43, 40, 45, 42, 47, 44, 49, 46, 51, 48, 53, 50, 55, 52, 57, 54, 59, 56, 61, 58, 63, 60, 65, 62, 67, 64, 69, 66, 71, 68, 73, 70

Offset: 0

Author

Mick Purcell (mickpurcell(AT)gmail.com), Sep 26 2009

Keywords

• nonn
• easy

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.

Examples

			For n = 3, Nimsum(3 + 4 + 5) = 2, as shown: 011 XOR 100 XOR 101 010.
		

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A065168. - R. J. Mathar, Sep 28 2009

Programs

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 *)

PARI

Vec((2*x^2-3*x+3)/((x-1)^2*(x+1)) + O(x^100)) \\ Colin Barker, Nov 05 2015

Python

n = 0
while n < 100:
    print(n^(n+1)^(n+2), end=',')
    n += 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

Extensions

Extended by R. J. Mathar, Sep 28 2009