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A075311
a(1) = 1; for n > 1, a(n) is the smallest number m > a(n-1) such that the number of 1's in the binary expansion of m is not already in the sequence.
5
1, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39, 40, 43, 45, 46, 48, 51, 53, 54, 57, 58, 60, 65, 66, 68, 71, 72, 75, 77, 78, 80, 83, 85, 86, 89, 90, 92, 96, 99, 101, 102, 105, 106, 108, 113, 114, 116, 120, 127, 129, 130, 132, 135, 136, 139, 141
OFFSET
1,2
COMMENTS
If A000120(k) is in the sequence then k is not.
Differs from A001969: 63 is not included since it has 6 bits set.
LINKS
Jon Perry and Phil Carmody, New sieve and a challenge, digest of 4 messages in primenumbers Yahoo group, Oct 11, 2002.
EXAMPLE
We start with a(1)=1. Then 2 is not included since it has one bit set and 1 is in the sequence. Next, 3 is included since it has 2 one bits and 2 is not in the sequence. And so on.
PROG
(PARI) v=vector(1000): v[1]=1: for(curr=2, 1000, e=A000120(curr): if(v[e], continue, v[curr]=1)): for(k=1, 1000, if(v[k], print1(k", ")))
(Haskell)
a075311 n = a075311_list !! (n-1)
a075311_list = 1 : f 2 [1] where
f x ys = if a000120 x `elem` ys then f (x + 1) ys
else x : f (x + 1) (x : ys)
-- _Reinhard Zumkeller_, Apr 22 2012
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
_Phil Carmody_, Oct 11 2002
EXTENSIONS
Edited by _Ralf Stephan_, Sep 14 2003
STATUS
approved