A004462 Nimsum n + 21.

21, 20, 23, 22, 17, 16, 19, 18, 29, 28, 31, 30, 25, 24, 27, 26, 5, 4, 7, 6, 1, 0, 3, 2, 13, 12, 15, 14, 9, 8, 11, 10, 53, 52, 55, 54, 49, 48, 51, 50, 61, 60, 63, 62, 57, 56, 59, 58, 37, 36, 39, 38, 33, 32, 35, 34, 45, 44, 47, 46, 41, 40, 43, 42, 85, 84, 87

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 (1,1,-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)

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

Sequence in context: A105706 A022977 A023463 * A195033 A267147 A154352

Adjacent sequences: A004459 A004460 A004461 * A004463 A004464 A004465

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved