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A010062
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a(0)=1; thereafter a(n+1) = a(n) + number of 1's in binary representation of a(n).
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34
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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)
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OFFSET
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0,2
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COMMENTS
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LINKS
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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).
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FORMULA
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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]
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EXAMPLE
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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.
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MATHEMATICA
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NestList[# + DigitCount[#, 2, 1] &, 1, 60] (* Alonso del Arte, Oct 26 2012 *)
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PROG
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(Haskell)
a010062 n = a010062_list !! n
(Magma) [n le 1 select 1 else Self(n-1)+&+Intseq(Self(n-1), 2): n in [1..61]]; // Bruno Berselli, Oct 27 2012
(Python)
from itertools import islice
def agen():
an = 1
while True: yield an; an += an.bit_count()
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CROSSREFS
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For the base-10 analog see A004207.
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KEYWORD
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nonn,base,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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