login
This site is supported by donations to The OEIS Foundation.

 

Logo

The OEIS is looking to hire part-time people to help edit core sequences, upload scanned documents, process citations, fix broken links, etc. - Neil Sloane, njasloane@gmail.com

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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.

David Garth and Adam Gouge, Affinely Self-Generating Sets and Morphisms, Journal of Integer Sequences, 10 (2007) 1-13.

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-Fran├žois 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: A235032 A242925 A214913 * A104739 A192047 A274281

Adjacent sequences:  A052496 A052497 A052498 * A052500 A052501 A052502

KEYWORD

nonn,nice

AUTHOR

Henry Bottomley, Mar 15 2000

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified May 30 06:51 EDT 2017. Contains 287302 sequences.