login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A024629 n written in fractional base 3/2. 33
0, 1, 2, 20, 21, 22, 210, 211, 212, 2100, 2101, 2102, 2120, 2121, 2122, 21010, 21011, 21012, 21200, 21201, 21202, 21220, 21221, 21222, 210110, 210111, 210112, 212000, 212001, 212002, 212020, 212021, 212022, 212210, 212211, 212212, 2101100, 2101101 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A246435(n) = (number of digits in a(n)) = A055642(a(n)). - Reinhard Zumkeller, Sep 05 2014

The number of positive even n such that a(n) has k+1 digits is A005428(k). - Glen Whitney, Jul 09 2017

The position of the rightmost "2" digit in a(3k), k >= 1, appears to be A087088(k). - Peter Munn, Jun 24 2020 [updated Peter Munn, Jul 14 2020 for new A087088 offset]

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Matvey Borodin, Hannah Han, Kaylee Ji, Tanya Khovanova, Alexander Peng, David Sun, Isabel Tu, Jason Yang, William Yang, Kevin Zhang, and Kevin Zhao, Variants of Base 3 over 2, arXiv:1901.09818 [math.NT], 2019.

B. Chen, R. Chen, J. Guo, S. Lee et al, On Base 3/2 and its sequences, arXiv:1808.04304 [math.NT], 2018.

Tanya Khovanova and Kevin Wu, Base 3/2 and Greedily Partitioned Sequences, arXiv:2007.09705 [math.NT], 2020.

J. S. Tanton, A collection of research problems. [archived version]

FORMULA

To represent a number in base b, if a digit is >= b, subtract b and carry 1. In fractional base a/b, subtract a and carry b.

EXAMPLE

Representations of the first few numbers are:

   0 =         0

   1 =         1

   2 =         2

   3 =       2 0

   4 =       2 1

   5 =       2 2

   6 =     2 1 0

   7 =     2 1 1

   8 =     2 1 2

   9 =   2 1 0 0

  10 =   2 1 0 1

  11 =   2 1 0 2

  12 =   2 1 2 0

  13 =   2 1 2 1

  14 =   2 1 2 2

  15 = 2 1 0 1 0

[extended and reformatted by Peter Munn, Jun 27 2020]

MAPLE

a:= proc(n) `if`(n<1, 0, irem(n, 3, 'q')+a(2*q)*10) end:

seq(a(n), n=0..45);  # Alois P. Heinz, Jun 19 2018

MATHEMATICA

a[ n_] := If[ n < 1, 0, a[ Quotient[n, 3] 2] 10 + Mod[ n, 3]]; (* Michael Somos, Jun 18 2014 *)

PROG

(Sage)

def basepqExpansion(p, q, n):

    L, i = [n], 1

    while L[i-1] >= p:

        x=L[i-1]

        L[i-1]=x.mod(p)

        L.append(q*(x//p))

        i+=1

    L.reverse()

    return Integer(''.join(str(x) for x in L))

[basepqExpansion(3, 2, n) for n in [0..40]] # - Tom Edgar, Hailey R. Olafson, and James Van Alstine, Jun 17 2014; modified and corrected by G. C. Greubel, Aug 20 2019

(PARI) {a(n) = if( n<1, 0, a(n\3 * 2) * 10 + n%3)}; /* Michael Somos, Jun 18 2014 */

(Haskell)

a024629 0 = 0

a024629 n = 10 * a024629 (2 * n') + t where (n', t) = divMod n 3

-- Reinhard Zumkeller, Sep 05 2014

CROSSREFS

Cf. A081848, A087088, A246435 (string lengths), A244040 (digit sums).

Sequence in context: A338994 A217394 A072998 * A235500 A319953 A111193

Adjacent sequences:  A024626 A024627 A024628 * A024630 A024631 A024632

KEYWORD

nonn,base

AUTHOR

David W. Wilson

EXTENSIONS

Tanton link corrected by Charles R Greathouse IV, Oct 20 2008

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 24 17:57 EDT 2022. Contains 356946 sequences. (Running on oeis4.)