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A052499 If n is in the sequence then so are 2n and 4n-1. 3
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; text; internal format)
OFFSET
0,2
COMMENTS
Theorem (J.-P. Allouche, J. Shallit, G. Skordev): This sequence = 1 + A003754.
LINKS
J.-P. Allouche, J. Shallit and G. Skordev, Self-generating sets, integers with missing blocks and substitutions, Discrete Math. 292 (2005) 1-15.
David Garth and Adam Gouge, Affinely Self-Generating Sets and Morphisms, Journal of Integer Sequences, 10 (2007) 1-13.
Andreas M. Hinz and Paul K. Stockmeyer, Precious Metal Sequences and Sierpinski-Type Graphs, J. Integer Seq., Vol 25 (2022), Article 22.4.8.
T. Karki, A. Lacroix, M. Rigo, On the recognizability of self-generating sets, JIS 13 (2010) #10.2.2.
C. Kimberling, A Self-Generating Set and the Golden Mean, J. Integer Sequences, 3 (2000), #00.2.8.
FORMULA
a(A001911(n)) = 2^n.
EXAMPLE
a(9)=14 is in the sequence because 14=2*(4*(2*1)-1).
MATHEMATICA
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 *)
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
CROSSREFS
Sequence in context: A242925 A336444 A214913 * A104739 A192047 A274281
KEYWORD
nonn,nice
AUTHOR
Henry Bottomley, Mar 15 2000
STATUS
approved

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Last modified February 26 12:54 EST 2024. Contains 370352 sequences. (Running on oeis4.)