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Search: id:A004443
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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
(list; graph; listen)
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OFFSET
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0,1
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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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Index entries for sequences related to Nim-sums
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FORMULA
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G.f.: [2-x-2x^2+3x^3]/[(1-x)^2(1+x^2)]. - R. 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*prod[k=0..inf, 1+x^(2^e(k))], with sum[k=0..inf, 2^e(k)] = m. - R. Stephan, Apr 24 2004
a(n) = n + 2(-1)^[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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CROSSREFS
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Cf. A003987, A004442.
Sequence in context: A128888 A163575 A163465 this_sequence A008290 A059066 A059067
Adjacent sequences: A004440 A004441 A004442 this_sequence A004444 A004445 A004446
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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