A004451 Nimsum n + 10.

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

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

Table of n, a(n) for n=0..57.

Index entries for sequences related to Nim-sums

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1,0,0,0,-1,2,-2,2,-1).

Formula

a(n) = n + 2(-1)^floor(n/2) + 8(-1)^floor(n/8). - Mitchell Harris, Jan 10 2005

G.f.: (11*x^11-10*x^10+7*x^9-6*x^8-5*x^3+6*x^2-9*x+10) / ((x-1)^2*(x^2+1)*(x^8+1)). - Colin Barker, Jun 29 2014

Maple

A004451:=n->n + 2*(-1)^floor(n/2) + 8*(-1)^floor(n/8); seq(A004451(n), n=0..50); # Wesley Ivan Hurt, Jun 29 2014

Mathematica

Table[n + 2 (-1)^Floor[n/2] + 8 (-1)^Floor[n/8], {n, 0, 50}] (* Wesley Ivan Hurt, Jun 29 2014 *)
LinearRecurrence[{2, -2, 2, -1, 0, 0, 0, -1, 2, -2, 2, -1}, {10, 11, 8, 9, 14, 15, 12, 13, 2, 3, 0, 1}, 100] (* Harvey P. Dale, Jul 02 2019 *)

Prog

(Magma) [n + 2*(-1)^Floor(n/2) + 8*(-1)^Floor(n/8) : n in [0..50]]; // Wesley Ivan Hurt, Jun 29 2014

Crossrefs

Sequence in context: A105743 A105835 A083163 * A352390 A004499 A020509

Adjacent sequences: A004448 A004449 A004450 * A004452 A004453 A004454

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved