A004457 Nimsum n + 16.

16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90

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

Formula

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

From Colin Barker, Apr 13 2016: (Start)

a(n) = n XOR 16.

G.f.: (16-15*x-16*x^16+17*x^17) / ((1-x)^2*(1+x^16)).

(End)

Maple

f:=n->n+16*(-1)^floor(n/16);

Prog

(PARI) Vec((16-15*x-16*x^16+17*x^17)/((1-x)^2*(1+x^16)) + O(x^50)) \\ Colin Barker, Apr 13 2016
(Python)
def A004457(n): return n^16 # Chai Wah Wu, Jan 19 2023

Crossrefs

Sequence in context: A004505 A262460 A190582 * A248501 A115420 A250038

Adjacent sequences: A004454 A004455 A004456 * A004458 A004459 A004460

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved