A004449 Nimsum n + 8.

8, 9, 10, 11, 12, 13, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 24, 25, 26, 27, 28, 29, 30, 31, 16, 17, 18, 19, 20, 21, 22, 23, 40, 41, 42, 43, 44, 45, 46, 47, 32, 33, 34, 35, 36, 37, 38, 39, 56, 57, 58, 59, 60, 61, 62, 63, 48, 49, 50, 51, 52, 53, 54, 55, 72, 73, 74

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

Formula

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

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

a(n) = n XOR 8. - Michel Marcus, Apr 12 2016

Mathematica

Table[BitXor[n, 8], {n, 0, 70}] (* Bruno Berselli, Nov 22 2016 *)
LinearRecurrence[{2, -1, 0, 0, 0, 0, 0, -1, 2, -1}, {8, 9, 10, 11, 12, 13, 14, 15, 0, 1}, 80] (* Harvey P. Dale, Apr 07 2019 *)

Prog

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

Crossrefs

Sequence in context: A320304 A217292 A004164 * A168098 A020722 A046037

Adjacent sequences: A004446 A004447 A004448 * A004450 A004451 A004452

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved