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 (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).
FORMULA
a(n) = n + (-1)^n + 2(-1)^[n/2] + 4(-1)^[n/4] + 8(-1)^[n/8]. - Mitchell Harris, Jan 10 2005
From Colin Barker, Apr 13 2016: (Start)
a(n) = n XOR 15.
G.f.: (15-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15+16*x^16) / ((1-x)^2*(1+x)*(1+x^2)*(1+x^4)*(1+x^8)).
(End)
PROG
(PARI) Vec((15-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15+16*x^16)/((1-x)^2*(1+x)*(1+x^2)*(1+x^4)*(1+x^8)) + O(x^50)) \\ Colin Barker, Apr 13 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved