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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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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Theorem (J.-P. Allouche, J. Shallit, G. Skordev): This sequence = 1 + A003754.
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REFERENCES
| David Garth and Adam Gouge, Affinely Self-Generating Sets and Morphisms, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.5.
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LINKS
| R. Zumkeller, Table of n, a(n) for n = 0..10000
J.-P. Allouche, J. Shallit and G. Skordev, Self-generating sets, integers with missing blocks and substitutions, Discrete Math. 292 (2005) 1-15.
C. Kimberling, A Self-Generating Set and the Golden Mean, J. Integer Sequences, 3 (2000), #00.2.8.
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FORMULA
| a(A001911(n))=2^n
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EXAMPLE
| a(9)=14 is in the sequence because 14=2*(4*(2*1)-1)
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MATHEMATICA
| 1 + Select[ Range[0, 200], FreeQ[ IntegerDigits[#, 2], {___, 0, 0, ___} ] & ] (* From Jean-François Alcover, Jan 20 2012, after J.-P. Allouche *)
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PROG
| (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
-- Reinhard Zumkeller, Jul 06 2011
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CROSSREFS
| Sequence in context: A051602 A175413 A192048 * A104739 A192047 A050116
Adjacent sequences: A052496 A052497 A052498 * A052500 A052501 A052502
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KEYWORD
| nonn,nice
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Mar 15 2000
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