A004450 Nimsum n + 9.

9, 8, 11, 10, 13, 12, 15, 14, 1, 0, 3, 2, 5, 4, 7, 6, 25, 24, 27, 26, 29, 28, 31, 30, 17, 16, 19, 18, 21, 20, 23, 22, 41, 40, 43, 42, 45, 44, 47, 46, 33, 32, 35, 34, 37, 36, 39, 38, 57, 56, 59, 58, 61, 60, 63, 62, 49, 48, 51, 50, 53, 52, 55, 54, 73, 72, 75

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

Colin Barker, 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,-1,0,0,0,0,-1,1,1,-1).

Formula

a(n) = n + (-1)^n + 8*(-1)^floor(n/8). - Mitchell Harris, Jan 10 2005

G.f.: (9 - x - 6*x^2 - 7*x^8 - x^9 + 10*x^10)/((1 - x)^2*(1 + x)*(1 + x^8)). - Colin Barker, Apr 12 2016

a(n) = n XOR 9. - Michel Marcus, Apr 12 2016

Mathematica

Table[BitXor[n, 2], {n, 0, 70}] (* Bruno Berselli, Nov 22 2016 *)
LinearRecurrence[{1, 1, -1, 0, 0, 0, 0, -1, 1, 1, -1}, {9, 8, 11, 10, 13, 12, 15, 14, 1, 0, 3}, 100] (* Harvey P. Dale, May 09 2018 *)

Prog

(PARI) Vec((9-x-6*x^2-7*x^8-x^9+10*x^10)/((1-x)^2*(1+x)*(1+x^8)) + O(x^50)) \\ Colin Barker, Apr 12 2016
(Magma) [BitwiseXor(n, 9): n in [0..70]]; // Bruno Berselli, Nov 22 2016

Crossrefs

Sequence in context: A046267 A343765 A019327 * A272962 A137392 A307639

Adjacent sequences: A004447 A004448 A004449 * A004451 A004452 A004453

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved