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!)
A304274 The concatenation of the first n elements is the largest positive even number with n digits when written in base 3/2. 3
2, 1, 2, 2, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence is possible due to the fact that the largest even integers are prefixes of each other.

A304272(n) is the largest even integer with n digits.

LINKS

Table of n, a(n) for n=1..105.

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

FORMULA

a(n) = A304273(n+1) + 1.

From Alois P. Heinz, Jun 21 2018: (Start)

a(n) = A305498(n+1) -3/2*A305498(n) + 1.

Sum_{i=0..n-1} (3/2)^i*a(n-i) = A305497(n). (End)

EXAMPLE

Number 8 in base 3/2 is 212, and it is the largest even integer with 3 digits in base 3/2. Its prefix 21 is 4: the largest even integer with 2 digits in base 3/2.

MAPLE

b:= proc(n) option remember; `if`(n=1, 2,

      (t-> t+irem(t, 2))(b(n-1)*3/2))

    end:

a:= n-> b(n+1)-3/2*b(n)+1:

seq(a(n), n=1..120);  # Alois P. Heinz, Jun 21 2018

MATHEMATICA

b[n_] := b[n] = If[n == 1, 2, Function[t, t + Mod[t, 2]][3/2 b[n-1]]];

a[n_] := b[n+1] - 3/2 b[n] + 1;

Array[a, 120] (* Jean-Fran├žois Alcover, Dec 13 2018, after Alois P. Heinz *)

CROSSREFS

Cf. A005428, A070885, A073941, A081848, A024629, A246435, A304024, A304025, A303500, A304272, A304273, A305497, A305498.

Sequence in context: A025917 A135689 A029438 * A081592 A255934 A085028

Adjacent sequences:  A304271 A304272 A304273 * A304275 A304276 A304277

KEYWORD

nonn,base

AUTHOR

Tanya Khovanova and PRIMES STEP Senior group, May 09 2018

EXTENSIONS

More terms from Alois P. Heinz, Jun 21 2018

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 October 6 12:00 EDT 2022. Contains 357264 sequences. (Running on oeis4.)