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 A006364 Numbers n with an even number of 1's in binary, ignoring last bit. (Formerly M4060) 2
 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)
 OFFSET 1,3 COMMENTS 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 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). 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 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, Oct 17 2003 Conjecture: a(n) = 2*n + (-1)^(n-A000120(n-1)) - (3+(-1)^n)/2. - Velin Yanev, Dec 21 2016 EXAMPLE G.f. = x + 6*x^2 + 7*x^3 + 10*x^4 + 11*x^5 + 12*x^6 + 13*x^7 + 18*x^8 + ... MATHEMATICA 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 *) 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) (PARI) is(n)=hammingweight(n>>1)%2==0 \\ Charles R Greathouse IV, Jun 19 2013 (Haskell) a006364 n = a006364_list a006364_list = filter (even . a000120. (`div` 2)) [0..] -- Reinhard Zumkeller, Oct 03 2011 CROSSREFS Sequence in context: A164989 A286473 A165363 * A037301 A163247 A085267 Adjacent sequences:  A006361 A006362 A006363 * A006365 A006366 A006367 KEYWORD base,nonn,nice,easy AUTHOR STATUS approved

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