A004446 a(n) = Nimsum n + 5.

5, 4, 7, 6, 1, 0, 3, 2, 13, 12, 15, 14, 9, 8, 11, 10, 21, 20, 23, 22, 17, 16, 19, 18, 29, 28, 31, 30, 25, 24, 27, 26, 37, 36, 39, 38, 33, 32, 35, 34, 45, 44, 47, 46, 41, 40, 43, 42, 53, 52, 55, 54, 49, 48, 51, 50, 61, 60

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

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for sequences related to Nim-sums

Index entries for linear recurrences with constant coefficients, signature (1,1,-1,-1,1,1,-1).

Formula

a(n) = n + (-1)^n + 4*(-1)^floor(n/4). - Mitchell Harris, Jan 10 2005

G.f.: (6*x^6 - x^5 - 3*x^4 - 2*x^2 - x + 5)/((x - 1)^2*(x + 1)*(x^4 + 1)). - Colin Barker, Jun 29 2014

Mathematica

CoefficientList[Series[(6 x^6 - x^5 - 3 x^4 - 2 x^2 - x + 5)/((x - 1)^2 (x + 1) (x^4 + 1)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 30 2014 *)
Table[BitXor[n, 5], {n, 0, 70}] (* Bruno Berselli, Nov 22 2016 *)

Prog

(PARI) Vec((6*x^6-x^5-3*x^4-2*x^2-x+5)/((x-1)^2*(x+1)*(x^4+1)) + O(x^100)) \\ Colin Barker, Jun 29 2014
(Magma) [BitwiseXor(n, 5): n in [0..70]]; // Bruno Berselli, Nov 22 2016

Crossrefs

Sequence in context: A195428 A254373 A343564 * A115409 A010775 A010485

Adjacent sequences: A004443 A004444 A004445 * A004447 A004448 A004449

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved