A004453 Nimsum n + 12.

12, 13, 14, 15, 8, 9, 10, 11, 4, 5, 6, 7, 0, 1, 2, 3, 28, 29, 30, 31, 24, 25, 26, 27, 20, 21, 22, 23, 16, 17, 18, 19, 44, 45, 46, 47, 40, 41, 42, 43, 36, 37, 38, 39, 32, 33, 34, 35, 60, 61, 62, 63, 56, 57, 58, 59, 52, 53, 54, 55, 48, 49, 50, 51, 76, 77, 78

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 (2,-1,0,-1,2,-1,0,-1,2,-1,0,-1,2,-1).

Formula

a(n) = n + 4*(-1)^floor(n/4) + 8*(-1)^floor(n/8). - Mitchell Harris, Jan 10 2005

G.f.: (12 - 11*x + 4*x^4 - 3*x^5 - 4*x^8 + 5*x^9 - 12*x^12 + 13*x^13)/((1 - x)^2*(1 + x^4)*(1 + x^8)). - Colin Barker, Apr 12 2016

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

Mathematica

Table[n + 4 (-1)^Floor[n / 4] + 8 (-1)^Floor[n / 8], {n, 0, 80}] (* Vincenzo Librandi, Nov 22 2016 *)

Prog

(PARI) Vec((12-11*x+4*x^4-3*x^5-4*x^8+5*x^9-12*x^12+13*x^13)/((1-x)^2*(1+x^4)*(1+x^8)) + O(x^50)) \\ Colin Barker, Apr 12 2016
(Magma) [BitwiseXor(n, 12): n in [0..70]]; // Bruno Berselli, Nov 22 2016

Crossrefs

Sequence in context: A020511 A008939 A284372 * A004501 A071955 A267760

Adjacent sequences: A004450 A004451 A004452 * A004454 A004455 A004456

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved