A004459 Nimsum n + 18.

18, 19, 16, 17, 22, 23, 20, 21, 26, 27, 24, 25, 30, 31, 28, 29, 2, 3, 0, 1, 6, 7, 4, 5, 10, 11, 8, 9, 14, 15, 12, 13, 50, 51, 48, 49, 54, 55, 52, 53, 58, 59, 56, 57, 62, 63, 60, 61, 34, 35, 32, 33, 38, 39, 36, 37, 42, 43, 40, 41, 46, 47, 44, 45, 82, 83, 80

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

Formula

a(n) = n + 2(-1)^[n/2] + 16(-1)^[n/16]. - Mitchell Harris, Jan 10 2005

From Colin Barker, Apr 13 2016: (Start)

a(n) = n XOR 18.

G.f.: (18-17*x+14*x^2-13*x^3-14*x^16+15*x^17-18*x^18+19*x^19) / ((1-x)^2*(1+x^2)*(1+x^16)).

(End)

Mathematica

CoefficientList[Series[(18-17x+14x^2-13x^3-14x^16+15x^17-18x^18+19x^19)/((1-x)^2(1+x^2)(1+x^16)), {x, 0, 100}], x] (* Harvey P. Dale, Jul 30 2025 *)
(* Alternative: *)
LinearRecurrence[{2, -2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -2, 2, -1}, {18, 19, 16, 17, 22, 23, 20, 21, 26, 27, 24, 25, 30, 31, 28, 29, 2, 3, 0, 1}, 100] (* Harvey P. Dale, Jul 30 2025 *)

Prog

(PARI) Vec((18-17*x+14*x^2-13*x^3-14*x^16+15*x^17-18*x^18+19*x^19)/((1-x)^2*(1+x^2)*(1+x^16)) + O(x^50)) \\ Colin Barker, Apr 13 2016

Crossrefs

Sequence in context: A177014 A355045 A357800 * A347282 A004507 A296760

Adjacent sequences: A004456 A004457 A004458 * A004460 A004461 A004462

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved