A004463 Nimsum n + 22.

22, 23, 20, 21, 18, 19, 16, 17, 30, 31, 28, 29, 26, 27, 24, 25, 6, 7, 4, 5, 2, 3, 0, 1, 14, 15, 12, 13, 10, 11, 8, 9, 54, 55, 52, 53, 50, 51, 48, 49, 62, 63, 60, 61, 58, 59, 56, 57, 38, 39, 36, 37, 34, 35, 32, 33, 46, 47, 44, 45, 42, 43, 40, 41, 86, 87, 84

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 (2,-2,2,-2,2,-2,2,-1,0,0,0,0,0,0,0,-1,2,-2,2,-2,2,-2,2,-1).

Formula

a(n) = n + 2(-1)^[n/2] + 4(-1)^[n/4] + 16(-1)^[n/16]. - Mitchell Harris, Jan 10 2005

From Colin Barker, Apr 14 2016: (Start)

a(n) = n XOR 22.

G.f.: (22 -21*x +18*x^2 -17*x^3 +14*x^4 -13*x^5 +10*x^6 -9*x^7 -10*x^16 +11*x^17 -14*x^18 +15*x^19 -18*x^20 +19*x^21 -22*x^22 +23*x^23) / ((1 -x)^2*(1 +x^2)*(1 +x^4)*(1 +x^16)).

(End)

a(n+32) = a(n)+32. - Robert Israel, Nov 22 2016

Maple

seq(Bits:-Xor(n, 22), n=0..100); # Robert Israel, Nov 22 2016

Prog

(PARI) Vec((22 -21*x +18*x^2 -17*x^3 +14*x^4 -13*x^5 +10*x^6 -9*x^7 -10*x^16 +11*x^17 -14*x^18 +15*x^19 -18*x^20 +19*x^21 -22*x^22 +23*x^23) / ((1 -x)^2*(1 +x^2)*(1 +x^4)*(1 +x^16)) + O(x^50)) \\ Colin Barker, Apr 14 2016

Crossrefs

Sequence in context: A223821 A048429 A336827 * A152835 A004511 A296763

Adjacent sequences: A004460 A004461 A004462 * A004464 A004465 A004466

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved