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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; internal format)
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OFFSET
| 1,3
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REFERENCES
| J.-P. Allouche and J. Shallit, The ring of k-regular sequences, II, Theoret. Computer Sci., 307 (2003), 3-29.
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
| Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
J.-P. Allouche and J. Shallit, The Ring of k-regular Sequences, II
Index entries for sequences related to binary expansion of n
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FORMULA
| 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 (ralf(AT)ark.in-berlin.de), Oct 17 2003
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MATHEMATICA
| Select[Range[0, 150], EvenQ[Count[Most[IntegerDigits[#, 2]], 1]]&] (* From Harvey P. Dale, Nov 03 2011 *)
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PROG
| (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)) (from Ralf Stephan)
(Haskell)
a006364 n = a006364_list
a006364_list = filter (even . a000120. (`div` 2)) [0..]
-- Reinhard Zumkeller, Oct 03 2011
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CROSSREFS
| Sequence in context: A032456 A164989 A165363 * A037301 A163247 A085267
Adjacent sequences: A006361 A006362 A006363 * A006365 A006366 A006367
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KEYWORD
| base,nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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