A004452 Nimsum n + 11.

11, 10, 9, 8, 15, 14, 13, 12, 3, 2, 1, 0, 7, 6, 5, 4, 27, 26, 25, 24, 31, 30, 29, 28, 19, 18, 17, 16, 23, 22, 21, 20, 43, 42, 41, 40, 47, 46, 45, 44, 35, 34, 33, 32, 39, 38, 37, 36, 59, 58, 57, 56, 63, 62, 61, 60, 51, 50, 49, 48, 55, 54, 53, 52, 75, 74, 73

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

Formula

a(n) = n + (-1)^n + 2*(-1)^floor(n/2) + 8*(-1)^floor(n/8). - Mitchell Harris, Jan 10 2005

G.f.: (11 - x - x^2 - x^3 - 4*x^4 - 5*x^8 - x^9 - x^10 - x^11 + 12*x^12)/((1 - x)^2*(1 + x)*(1 + x^2)*(1 + x^8)). - Colin Barker, Apr 12 2016

a(n) = A003987(n, 11). - Michel Marcus, Nov 10 2021

Mathematica

Table[BitXor[n, 11], {n, 0, 70}] (* Bruno Berselli, Nov 22 2016 *)

Prog

(PARI) Vec((11-x-x^2-x^3-4*x^4-5*x^8-x^9-x^10-x^11+12*x^12)/((1-x)^2*(1+x)*(1+x^2)*(1+x^8)) + O(x^50)) \\ Colin Barker, Apr 12 2016
(PARI) a(n) = n + (-1)^n + 2*(-1)^(n\2) + 8*(-1)^(n\8); \\ Michel Marcus, Apr 12 2016
(Magma) [BitwiseXor(n, 11): n in [0..70]]; // Bruno Berselli, Nov 22 2016
(Python)
def a(n): return n^11
print([a(n) for n in range(67)]) # Michael S. Branicky, Nov 10 2021

Crossrefs

Cf. A003987.

Sequence in context: A261304 A055122 A279650 * A291467 A112952 A343959

Adjacent sequences: A004449 A004450 A004451 * A004453 A004454 A004455

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved