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2, 3, 0, 1, 6, 7, 4, 5, 10, 11, 8, 9, 14, 15, 12, 13, 18, 19, 16, 17, 22, 23, 20, 21, 26, 27, 24, 25, 30, 31, 28, 29, 34, 35, 32, 33, 38, 39, 36, 37, 42, 43, 40, 41, 46, 47, 44, 45, 50, 51, 48, 49, 54, 55, 52, 53, 58, 59, 56, 57, 62, 63, 60, 61, 66, 67, 64, 65
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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A self-inverse permutation of the natural numbers. - Philippe Deléham, Nov 22 2016
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REFERENCES
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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.
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LINKS
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FORMULA
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G.f.: (2-x-2x^2+3x^3)/((1-x)^2(1+x^2)). - Ralf Stephan, Apr 24 2004
The sequences 'Nimsum n + m' seem to have the general o.g.f. p(x)/q(x) with p, q polynomials and q(x) = (1-x)^2*Product_{k>=0} (1+x^(2^e(k))), with Sum_{k>=0} 2^e(k) = m. - Ralf Stephan, Apr 24 2004
a(n) = n + 2(-1)^floor(n/2). - Mitchell Harris, Jan 10 2005
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MAPLE
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nimsum := proc(a, b) local t1, t2, t3, t4, l; t1 := convert(a+2^200, base, 2); t2 := convert(b+2^200, base, 2); t3 := evalm(t1+t2); map(x->x mod 2, t3); t4 := convert(evalm(%), list); l := convert(t4, base, 2, 10); sum(l[k]*10^(k-1), k=1..nops(l)); end;
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MATHEMATICA
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Table[BitXor[n, 2], {n, 0, 100}] (* T. D. Noe, Feb 09 2013 *)
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PROG
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(Python) for n in range(20): print(2^n) # Oliver Knill, Feb 16 2020
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CROSSREFS
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Essentially the same as A256008 - 1.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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