A004456 Nimsum n + 15.

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

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 (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).

Formula

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

From Colin Barker, Apr 13 2016: (Start)

a(n) = n XOR 15.

G.f.: (15-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15+16*x^16) / ((1-x)^2*(1+x)*(1+x^2)*(1+x^4)*(1+x^8)).

(End)

Prog

(PARI) Vec((15-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10-x^11-x^12-x^13-x^14-x^15+16*x^16)/((1-x)^2*(1+x)*(1+x^2)*(1+x^4)*(1+x^8)) + O(x^50)) \\ Colin Barker, Apr 13 2016

Crossrefs

Sequence in context: A343924 A022971 A023457 * A055126 A182336 A273369

Adjacent sequences: A004453 A004454 A004455 * A004457 A004458 A004459

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved