A004460 Nimsum n + 19.

19, 18, 17, 16, 23, 22, 21, 20, 27, 26, 25, 24, 31, 30, 29, 28, 3, 2, 1, 0, 7, 6, 5, 4, 11, 10, 9, 8, 15, 14, 13, 12, 51, 50, 49, 48, 55, 54, 53, 52, 59, 58, 57, 56, 63, 62, 61, 60, 35, 34, 33, 32, 39, 38, 37, 36, 43, 42, 41, 40, 47, 46, 45, 44, 83, 82, 81

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

Paolo Xausa, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Colin Barker).

Index entries for sequences related to Nim-sums

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,-1,1,0,0,1,-1).

Formula

a(n) = n + (-1)^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 19.

G.f.: (19-x-x^2-x^3-12*x^4-13*x^16-x^17-x^18-x^19+20*x^20) / ((1-x)^2*(1+x)*(1+x^2)*(1+x^16)). (End)

Mathematica

BitXor[Range[0, 100], 19] (* Paolo Xausa, Apr 20 2026 *)

Prog

(PARI) Vec((19-x-x^2-x^3-12*x^4-13*x^16-x^17-x^18-x^19+20*x^20)/((1-x)^2*(1+x)*(1+x^2)*(1+x^16)) + O(x^50)) \\ Colin Barker, Apr 13 2016

Crossrefs

Sequence in context: A022975 A023461 A305238 * A082126 A176411 A131382

Adjacent sequences: A004457 A004458 A004459 * A004461 A004462 A004463

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved