A004448 Nimsum n + 7.

7, 6, 5, 4, 3, 2, 1, 0, 15, 14, 13, 12, 11, 10, 9, 8, 23, 22, 21, 20, 19, 18, 17, 16, 31, 30, 29, 28, 27, 26, 25, 24, 39, 38, 37, 36, 35, 34, 33, 32, 47, 46, 45, 44, 43, 42, 41, 40, 55, 54, 53, 52, 51, 50, 49, 48, 63, 62, 61, 60, 59, 58, 57, 56, 71, 70, 69, 68, 67, 66, 65, 64, 79, 78, 77, 76, 75, 74, 73, 72, 87, 86, 85

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for sequences related to Nim-sums
• Index entries for sequences that are permutations of the natural numbers
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,1,-1).

Programs

Maple

A004448:=n->n+(-1)^n+2*(-1)^floor(n/2)+4*(-1)^floor(n/4): seq(A004448(n), n=0..100); # Wesley Ivan Hurt, Apr 28 2017

Mathematica

CoefficientList[Series[(8 x^8 - x^7 - x^6 - x^5 - x^4 - x^3 - x^2 - x + 7)/((x - 1)^2 (x + 1) (x^2 + 1) (x^4 + 1)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 30 2014 *)

PARI

Vec((8*x^8-x^7-x^6-x^5-x^4-x^3-x^2-x+7)/((x-1)^2*(x+1)*(x^2+1)*(x^4+1)) + O(x^100)) \\ Colin Barker, Jun 29 2014

Python

def a(n): return n^7
print([a(n) for n in range(83)]) # Michael S. Branicky, Jul 06 2021

Formula

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

G.f.: (8*x^8-x^7-x^6-x^5-x^4-x^3-x^2-x+7) / ((x-1)^2*(x+1)*(x^2+1)*(x^4+1)). - Colin Barker, Jun 29 2014

Extensions

More terms from Colin Barker, Jun 29 2014