A052499 If n is in the sequence then so are 2n and 4n-1.
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
Offset: 0
Examples
a(9)=14 is in the sequence because 14=2*(4*(2*1)-1).
Links
- Reinhard 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.
- 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.
Programs
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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 -- Reinhard Zumkeller, Jul 06 2011 -
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 *) -
Python
from itertools import count, islice def A052499_gen(startvalue=1): # generator of terms >= startvalue return filter(lambda n: not '00' in bin(n-1),count(max(startvalue,1))) A052499_list = list(islice(A052499_gen(),20)) # Chai Wah Wu, Feb 12 2025
Formula
a(A001911(n)) = 2^n.
Comments