A004447 Nimsum n + 6.

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

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 (2,-2,2,-2,2,-2,2,-1).

Formula

a(n) = n + 2*(-1)^floor(n/2) + 4*(-1)^floor(n/4). - Mitchell Harris, Jan 10 2005

G.f.: (7*x^7 - 6*x^6 + 3*x^5 - 2*x^4 - x^3 + 2*x^2 - 5*x + 6)/((x - 1)^2*(x^2 + 1)*(x^4 + 1)). - Colin Barker, Jun 29 2014

Mathematica

CoefficientList[Series[(7 x^7 - 6 x^6 + 3 x^5 - 2 x^4 - x^3 + 2 x^2 - 5 x + 6)/((x - 1)^2 (x^2 + 1) (x^4 + 1)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 30 2014 *)
Table[BitXor[n, 6], {n, 0, 70}] (* Bruno Berselli, Nov 22 2016 *)
LinearRecurrence[{2, -2, 2, -2, 2, -2, 2, -1}, {6, 7, 4, 5, 2, 3, 0, 1}, 70] (* Harvey P. Dale, Sep 30 2017 *)

Prog

(PARI) Vec((7*x^7-6*x^6+3*x^5-2*x^4-x^3+2*x^2-5*x+6)/((x-1)^2*(x^2+1)*(x^4+1)) + O(x^100)) \\ Colin Barker, Jun 29 2014
(Magma) [BitwiseXor(n, 6): n in [0..70]]; // Bruno Berselli, Nov 22 2016

Crossrefs

Sequence in context: A195776 A092678 A019932 * A258989 A005351 A098882

Adjacent sequences: A004444 A004445 A004446 * A004448 A004449 A004450

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved