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 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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved