A004464 Nimsum n + 23.

23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8, 55, 54, 53, 52, 51, 50, 49, 48, 63, 62, 61, 60, 59, 58, 57, 56, 39, 38, 37, 36, 35, 34, 33, 32, 47, 46, 45, 44, 43, 42, 41, 40, 87, 86, 85

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

Formula

a(n) = n + (-1)^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 23.

G.f.: (23 -x -x^2 -x^3 -x^4 -x^5 -x^6 -x^7 -8*x^8 -9*x^16 -x^17 -x^18 -x^19 -x^20 -x^21 -x^22 -x^23 +24*x^24) / ((1 -x)^2*(1 +x)*(1 +x^2)*(1 +x^4)*(1 +x^16)).

(End)

Prog

(PARI) Vec((23 -x -x^2 -x^3 -x^4 -x^5 -x^6 -x^7 -8*x^8 -9*x^16 -x^17 -x^18 -x^19 -x^20 -x^21 -x^22 -x^23 +24*x^24) / ((1 -x)^2*(1 +x)*(1 +x^2)*(1 +x^4)*(1 +x^16)) + O(x^50)) \\ Colin Barker, Apr 14 2016

Crossrefs

Sequence in context: A261308 A022979 A023465 * A255228 A255221 A072135

Adjacent sequences: A004461 A004462 A004463 * A004465 A004466 A004467

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved