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 A010062 a(0)=1; thereafter a(n+1) = a(n) + number of 1's in binary representation of a(n). 29
 1, 2, 3, 5, 7, 10, 12, 14, 17, 19, 22, 25, 28, 31, 36, 38, 41, 44, 47, 52, 55, 60, 64, 65, 67, 70, 73, 76, 79, 84, 87, 92, 96, 98, 101, 105, 109, 114, 118, 123, 129, 131, 134, 137, 140, 143, 148, 151, 156, 160, 162, 165, 169, 173, 178, 182, 187, 193, 196, 199, 204 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 Raoul Nakhmanson-Kulish, Graph of a(n)/(n*log_2(n)/2), showing self-similar fractal structure. Raoul Nakhmanson-Kulish, Graph of f(n), where f(n) = (a(n)-n*log_2(n)/2)/(n*sqrt(log_2(n)*log_2 log_2(n))) (see Stolarsky's estimate below). Kenneth B. Stolarsky, The sum of a digitaddition series, Proc. Amer. Math. Soc. 59 (1976), no. 1, 1--5. MR0409340 (53 #13099) FORMULA a(n) = (n/2)*log n + O(n*sqrt(log n * loglog n)), where log means log_2. In particular, a(n) ~ (n/2)*log n. [Stolarsky] a(n + 1) = A092391(a(n)) = a(n) + A000120(a(n)). - Reinhard Zumkeller, May 27 2012, May 08 2004; corrected thanks to a notice by Lambert Herrgesell EXAMPLE a(7) = 14 because a(6) = 12, which is 1100 in binary (having 2 on bits), and 12 + 2 = 14. a(8) = 17 because a(7) = 14, which is 1110 in binary (having 3 on bits), and 14 + 3 = 17. MATHEMATICA NestList[# + DigitCount[#, 2, 1] &, 1, 60] (* Alonso del Arte, Oct 26 2012 *) PROG (PARI) s=1; for(n=1, 100, s=s+sum(i=1, length(binary(s)), component(binary(s), i)); print1(s, ", ")) (PARI) print1(s=1); for(n=2, 30, print1(", ", s+=hammingweight(s))) \\ Charles R Greathouse IV, Oct 27 2012 (Haskell) a010062 n = a010062_list !! n a010062_list = iterate a092391 1  -- Reinhard Zumkeller, May 13 2012 (MAGMA) [n le 1 select 1 else Self(n-1)+&+Intseq(Self(n-1), 2): n in [1..61]]; // Bruno Berselli, Oct 27 2012 CROSSREFS First row of A228083. For the base-10 analog see A004207. Cf. A010061, A092391, A229167, A096303, A229743, A229744, A230297 (this sequence written in binary), A230298 (read mod 2). See A230088 for partial sums. Sequence in context: A254860 A144726 A123885 * A119565 A119592 A191892 Adjacent sequences:  A010059 A010060 A010061 * A010063 A010064 A010065 KEYWORD nonn,base,easy,nice AUTHOR Leonid Broukhis, Mar 15 1996 EXTENSIONS More terms from Benoit Cloitre, Jun 02 2002 Stolarsky reference from Matthew C. Russell, Oct 08 2013 STATUS approved

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Last modified June 19 08:41 EDT 2018. Contains 305581 sequences. (Running on oeis4.)