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 (1,1,-1,-1,1,1,-1,0,0,0,0,0,0,0,0,-1,1,1,-1,-1,1,1,-1).
FORMULA
a(n) = n + (-1)^n + 4*(-1)^[n/4] + 16*(-1)^[n/16]. - Mitchell Harris, Jan 10 2005
From Colin Barker, Apr 13 2016: (Start)
a(n) = n XOR 21.
G.f.: (21-x-18*x^2+13*x^4-x^5-10*x^6-11*x^16-x^17+14*x^18-19*x^20-x^21+22*x^22) / ((1-x)^2*(1+x)*(1+x^4)*(1+x^16)). (End)
MATHEMATICA
BitXor[Range[0, 100], 21] (* Paolo Xausa, Apr 20 2026 *)
PROG
(PARI) Vec((21-x-18*x^2+13*x^4-x^5-10*x^6-11*x^16-x^17+14*x^18-19*x^20-x^21+22*x^22)/((1-x)^2*(1+x)*(1+x^4)*(1+x^16)) + O(x^50)) \\ Colin Barker, Apr 13 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved
