A304023 -id:A304023 - cp's OEIS frontend

A304024 a(n) is the largest integer with n digits in base 3/2.

2, 22, 212, 2122, 21222, 212212, 2122112, 21221112, 212211122, 2122111222, 21221112212, 212211122122, 2122111221212, 21221112212112, 212211122121122, 2122111221211222, 21221112212112212, 212211122121122122

Offset: 0

Tanya Khovanova and PRIMES STEP Senior group, May 04 2018

Every number starts and ends with 2 and contains only twos and ones.
Removing the last digit produces sequence A304272 of the largest even integers in base 3/2.
The value of this sequence in base 10 is A304025.
When adding 1 to the value of this sequence we get A070885.
The largest integer with a given number of digits in base 3/2 can be produced directly from the smallest number, sequence A304023, by replacing 21 at the beginning and 0 at the end with 2, and by shifting the rest up by 1, see sequence A304023.

			The number 5 in base 3/2 is 22, and the number 6 is 210. Therefore, 22 is the largest two-digit integer.

Cf. A005428, A024629, A070885, A073941, A081848, A246435, A303500, A304023, A304025, A304272.

first(n) = {my(res=vector(n), c = 2); res[1]=2; for(i=2, n, res[i] = 10 * res[i-1] + 2; if(c % 2 == 1, res[i] -= 10); c = 3 * c / 2 + if(c%2==0, 2, 1/2)); res} \\ David A. Corneth, May 11 2018

a(1) = 2, for n > 1, a(n) = 10 * a(n - 1) + 2 if A304025(n - 1) is even. Otherwise, a(n) = 10 * a(n - 1) - 8. - David A. Corneth, May 11 2018

A305497 The largest positive even integer that can be represented with n digits in base 3/2.

Original entry on oeis.org

2, 4, 8, 14, 22, 34, 52, 80, 122, 184, 278, 418, 628, 944, 1418, 2128, 3194, 4792, 7190, 10786, 16180, 24272, 36410, 54616, 81926, 122890, 184336, 276506, 414760, 622142, 933214, 1399822, 2099734, 3149602, 4724404, 7086608, 10629914, 15944872, 23917310

Offset: 1

Tanya Khovanova and PRIMES STEP Senior group, Jun 02 2018

Michael De Vlieger, Table of n, a(n) for n = 1..1000
B. Chen, R. Chen, J. Guo, S. Lee et al., On Base 3/2 and its Sequences, arXiv:1808.04304 [math.NT], 2018.

Cf. A005428, A070885, A073941, A081848, A024629, A246435, A304023, A304024, A304025, A303500, A304272, A304273, A304274, A305498.

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; A305497[n_] := Sum[(3/2)^i*a[n - i], {i, 0, n - 1}]; Table[A305497[n], {n, 1, 39}] (* Robert P. P. McKone, Feb 12 2021 *)

from itertools import islice
def A305497_gen(): # generator of terms
    a = 2
    while True:
        a += a>>1
        yield (a<<1)-4
A305497_list = list(islice(A305497_gen(),70)) # Chai Wah Wu, Sep 20 2022

a(n+1) = 2*floor(3*a(n)/4) + 2.
a(n) = 2*A061419(n+1) - 2.
a(n) = A305498(n+1) - 2.
a(n) = Sum_{i=0..n-1} (3/2)^i*A304274(n-i). - Alois P. Heinz, Jun 21 2018

A305498 The smallest positive even integer that can be represented with n digits in base 3/2.

Original entry on oeis.org

2, 4, 6, 10, 16, 24, 36, 54, 82, 124, 186, 280, 420, 630, 946, 1420, 2130, 3196, 4794, 7192, 10788, 16182, 24274, 36412, 54618, 81928, 122892, 184338, 276508, 414762, 622144, 933216, 1399824, 2099736, 3149604, 4724406, 7086610, 10629916, 15944874, 23917312

Offset: 1

Tanya Khovanova and PRIMES STEP Senior group, Jun 02 2018

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

Cf. A005428, A070885, A073941, A081848, A024629, A246435, A304023, A304024, A304025, A303500, A304272, A304273, A304274, A305497.

from itertools import islice
def A305498_gen(): # generator of terms
    a = 2
    while True:
        yield (a<<1)-2
        a += a>>1
A305498_list = list(islice(A305498_gen(),70)) # Chai Wah Wu, Sep 20 2022

a(n+1) = 2*ceiling(3*a(n)/4).
a(n) = 2*A061419(n).
a(n) = A305497(n-1) + 2.

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A304024 a(n) is the largest integer with n digits in base 3/2.

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A305497 The largest positive even integer that can be represented with n digits in base 3/2.

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A305498 The smallest positive even integer that can be represented with n digits in base 3/2.

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Author

Keywords

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Crossrefs

Programs

Python

Formula