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A006364
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Numbers n with an even number of 1's in binary, ignoring last bit.
(Formerly M4060)
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2
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0, 1, 6, 7, 10, 11, 12, 13, 18, 19, 20, 21, 24, 25, 30, 31, 34, 35, 36, 37, 40, 41, 46, 47, 48, 49, 54, 55, 58, 59, 60, 61, 66, 67, 68, 69, 72, 73, 78, 79, 80, 81, 86, 87, 90, 91, 92, 93, 96, 97, 102, 103, 106, 107, 108, 109, 114, 115, 116, 117, 120, 121, 126, 127, 130, 131, 132
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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Equivalently, numbers n such that n has an odd number of 1's in binary if and only if n is odd. - Aaron Weiner, Jun 19 2013
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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. 111.
R. K. Guy, Impartial games, pp. 35-55 of Combinatorial Games, ed. R. K. Guy, Proc. Sympos. Appl. Math., 43, Amer. Math. Soc., 1991.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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Union of 2*A001969 and 2*A001969+1. With initial index 0: a(2n+1) = a(2n)+1, a(4n) = a(2n)+4n, a(4n+2) = -a(2n)+12n+6. - Ralf Stephan, Oct 17 2003
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EXAMPLE
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G.f. = x + 6*x^2 + 7*x^3 + 10*x^4 + 11*x^5 + 12*x^6 + 13*x^7 + 18*x^8 + ...
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MATHEMATICA
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Select[Range[0, 150], EvenQ[Count[Most[IntegerDigits[#, 2]], 1]]&] (* Harvey P. Dale, Nov 03 2011 *)
a[ n_] := Which[ n < 1, 0, Mod[n, 2] > 0, a[n - 1] + 1, Mod[n, 4] > 0, 3 n - a[n/2 - 1], True, n + a[n/2]]; (* Michael Somos, Dec 21 2016 *)
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PROG
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(PARI) a(n)=if(n<1, 0, if(n%2==0, if(n%4==0, a(n/2)+n, -a((n-2)/2)+3*n), a(n-1)+1)) \\ Ralf Stephan
(Haskell)
a006364 n = a006364_list
a006364_list = filter (even . a000120. (`div` 2)) [0..]
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CROSSREFS
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KEYWORD
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base,nonn,nice,easy
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AUTHOR
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STATUS
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approved
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