A004455 Nimsum n + 14.

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

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

Formula

a(n) = n + 2*(-1)^[n/2] + 4*(-1)^[n/4] + 8*(-1)^[n/8]. - Mitchell Harris, Jan 10 2005

G.f.: (14-13*x+10*x^2-9*x^3+6*x^4-5*x^5+2*x^6-x^7-2*x^8+3*x^9-6*x^10+7*x^11-10*x^12+11*x^13-14*x^14+15*x^15) / ((1-x)^2*(1+x^2)*(1+x^4)*(1+x^8)). - Colin Barker, Apr 12 2016

a(n) = n XOR 14, where XOR is the bitwise XOR operator. - Paolo Xausa, Apr 20 2026

Mathematica

BitXor[Range[0, 100], 14] (* Paolo Xausa, Apr 20 2026 *)

Prog

(PARI) Vec((14-13*x+10*x^2-9*x^3+6*x^4-5*x^5+2*x^6-x^7-2*x^8+3*x^9-6*x^10+7*x^11-10*x^12+11*x^13-14*x^14+15*x^15) / ((1-x)^2*(1+x^2)*(1+x^4)*(1+x^8)) + O(x^50)) \\ Colin Barker, Apr 12 2016

Crossrefs

Sequence in context: A134913 A176169 A168548 * A142865 A089838 A297278

Adjacent sequences: A004452 A004453 A004454 * A004456 A004457 A004458

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved