OFFSET
0,1
COMMENTS
A self-inverse permutation of the natural numbers. - Philippe Deléham, Nov 22 2016
REFERENCES
E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 60.
J. H. Conway, On Numbers and Games. Academic Press, NY, 1976, pp. 51-53.
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 0..20000
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), #P1.52.
Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).
FORMULA
a(n) = n XOR 2. - Joerg Arndt, Feb 07 2013
G.f.: (2-x-2x^2+3x^3)/((1-x)^2(1+x^2)). - Ralf Stephan, Apr 24 2004
The sequences 'Nimsum n + m' seem to have the general o.g.f. p(x)/q(x) with p, q polynomials and q(x) = (1-x)^2*Product_{k>=0} (1+x^(2^e(k))), with Sum_{k>=0} 2^e(k) = m. - Ralf Stephan, Apr 24 2004
a(n) = n + 2(-1)^floor(n/2). - Mitchell Harris, Jan 10 2005
a(n) = OR(n,2) - AND(n,2). - Gary Detlefs, Feb 06 2013
E.g.f.: 2*(sin(x) + cos(x)) + x*exp(x). - Ilya Gutkovskiy, Jul 01 2016
Sum_{n>=0,n<>2} (-1)^n/a(n) = -log(2) = -A002162. - Peter McNair, Aug 07 2023
MAPLE
nimsum := proc(a, b) local t1, t2, t3, t4, l; t1 := convert(a+2^200, base, 2); t2 := convert(b+2^200, base, 2); t3 := evalm(t1+t2); map(x->x mod 2, t3); t4 := convert(evalm(%), list); l := convert(t4, base, 2, 10); sum(l[k]*10^(k-1), k=1..nops(l)); end;
f := n -> n + 2*(-1)^floor(n/2); # N. J. A. Sloane, Jul 06 2019
MATHEMATICA
Table[BitXor[n, 2], {n, 0, 100}] (* T. D. Noe, Feb 09 2013 *)
PROG
(PARI) a(n)=bitxor(n, 2) \\ Charles R Greathouse IV, Oct 07 2015
(Python) for n in range(20): print(2^n) # Oliver Knill, Feb 16 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved