A004458 Nimsum n + 17.

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

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

Reinhard Zumkeller, 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,-1,0,0,0,0,0,0,0,0,0,0,0,0,-1,1,1,-1).

Formula

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

G.f.: (17-x-14*x^2-15*x^16-x^17+18*x^18) / ((1-x)^2*(1+x)*(1+x^16)). - Colin Barker, Apr 12 2016

a(n) = n XOR 17. - Michel Marcus, Apr 12 2016

Mathematica

BitXor[Range[0, 100], 17] (* Paolo Xausa, Apr 20 2026 *)

Prog

(Haskell)
import Data.Bits (xor)
a004458 n = n `xor` 17 :: Integer  -- Reinhard Zumkeller, Nov 07 2012
(PARI) Vec((17-x-14*x^2-15*x^16-x^17+18*x^18)/((1-x)^2*(1+x)*(1+x^16)) + O(x^50)) \\ Colin Barker, Apr 12 2016
(PARI) a(n) = n + (-1)^n + 16*(-1)^(n\16); \\ Michel Marcus, Apr 12 2016

Crossrefs

Cf. A004442.

Sequence in context: A261306 A022973 A023459 * A082123 A368929 A273973

Adjacent sequences: A004455 A004456 A004457 * A004459 A004460 A004461

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved