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A004454 Nimsum n + 13. 1
13, 12, 15, 14, 9, 8, 11, 10, 5, 4, 7, 6, 1, 0, 3, 2, 29, 28, 31, 30, 25, 24, 27, 26, 21, 20, 23, 22, 17, 16, 19, 18, 45, 44, 47, 46, 41, 40, 43, 42, 37, 36, 39, 38, 33, 32, 35, 34, 61, 60, 63, 62, 57, 56, 59, 58, 53, 52, 55, 54, 49, 48, 51, 50, 77, 76, 79 (list; graph; refs; listen; history; text; internal format)
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 (1,1,-1,-1,1,1,-1,-1,1,1,-1,-1,1,1,-1).

FORMULA

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

From Colin Barker, Apr 13 2016: (Start)

a(n) = n XOR 13.

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

(End)

PROG

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

CROSSREFS

Sequence in context: A055124 A212526 A019331 * A113548 A249998 A195210

Adjacent sequences:  A004451 A004452 A004453 * A004455 A004456 A004457

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 13 08:08 EST 2019. Contains 329968 sequences. (Running on oeis4.)