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A052499
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If n is in the sequence then so are 2n and 4n-1.
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3
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1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 15, 16, 22, 23, 24, 27, 28, 30, 31, 32, 43, 44, 46, 47, 48, 54, 55, 56, 59, 60, 62, 63, 64, 86, 87, 88, 91, 92, 94, 95, 96, 107, 108, 110, 111, 112, 118, 119, 120, 123, 124, 126, 127, 128, 171, 172, 174, 175, 176, 182, 183, 184, 187
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refs;
listen;
history;
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internal format)
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OFFSET
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0,2
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COMMENTS
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Theorem (J.-P. Allouche, J. Shallit, G. Skordev): This sequence = 1 + A003754.
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LINKS
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FORMULA
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EXAMPLE
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a(9)=14 is in the sequence because 14=2*(4*(2*1)-1).
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MATHEMATICA
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1 + Select[ Range[0, 200], FreeQ[ IntegerDigits[#, 2], {___, 0, 0, ___} ] & ] (* Jean-François Alcover, Jan 20 2012, after J.-P. Allouche *)
a[1] = 1; a[n_] := a[n] = a[n - 1] + Ceiling[2^IntegerExponent[a[n - 1], 2]/3]; Array[a, 200] (* Birkas Gyorgy, May 30 2012 *)
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PROG
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(Haskell)
import Data.Set (singleton, deleteFindMin, insert)
a052499 n = a052499_list !! n
a052499_list = f $ singleton 1 where
f s = m : f (insert (2*m) $ insert (4*m-1) s') where
(m, s') = deleteFindMin s
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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STATUS
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approved
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