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

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

1,1

Links

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.

Formula

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

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; 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 *)

Prog

(Python)
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

Crossrefs

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

Sequence in context: A025003 A087151 A053798 * A231429 A259392 A261968

Adjacent sequences: A305494 A305495 A305496 * A305498 A305499 A305500

Keyword

nonn,base

Author

Tanya Khovanova and PRIMES STEP Senior group, Jun 02 2018

Status

approved