A328727 -id:A328727 - cp's OEIS frontend

A328728 a(n) = Sum_{k = 0..w and t_k > 0} (-1)^t_k * 2^k, where Sum_{k = 0..w} t_k * 3^k is the ternary representation of A328727(n).

0, -1, 1, -2, 2, -4, -5, -3, 4, 3, 5, -8, -9, -7, -10, -6, 8, 7, 9, 6, 10, -16, -17, -15, -18, -14, -20, -21, -19, -12, -13, -11, 16, 15, 17, 14, 18, 12, 11, 13, 20, 19, 21, -32, -33, -31, -34, -30, -36, -37, -35, -28, -29, -27, -40, -41, -39, -42, -38, -24

Offset: 1

Rémy Sigrist, Oct 26 2019

Every integer appears once in the sequence.

Rémy Sigrist, Table of n, a(n) for n = 1..5461

Cf. A001045, A328727, A328749.

for (n=0, 297, t = Vecrev(digits(n,3)); if (sum(k=1, #t-1, t[k]*t[k+1])==0, print1 (sum(k=1, #t, if (t[k], 2^k*(-1)^t[k], 0)/2) ", ")))

from itertools import count, islice
from gmpy2 import digits
def A328728_gen(startvalue=0): # generator of terms >= startvalue
    for n in count(max(startvalue,0)):
        s = digits(n,3)
        for i in range(len(s)-1):
            if '0' not in s[i:i+2]:
                break
        else:
            yield sum((-(1<A328728_list = list(islice(A328728_gen(),20)) # Chai Wah Wu, Apr 12 2023

a(n) = A328749(A328727(n)).

Sum_{k = 1..n} a(k) = 0 iff n belongs to A001045.

A362089 The base-3 expansion of a(n) is obtained by inserting a zero before each nonzero digit of the base-3 expansion of n.

Original entry on oeis.org

0, 1, 2, 3, 10, 11, 6, 19, 20, 9, 28, 29, 30, 91, 92, 33, 100, 101, 18, 55, 56, 57, 172, 173, 60, 181, 182, 27, 82, 83, 84, 253, 254, 87, 262, 263, 90, 271, 272, 273, 820, 821, 276, 829, 830, 99, 298, 299, 300, 901, 902, 303, 910, 911, 54, 163, 164, 165, 496

Offset: 0

Rémy Sigrist, Apr 08 2023

This sequence is a permutation of A328727.

			The first terms, in decimal and in base-3, are:
  n   a(n)  ter(n)  ter(a(n))
  --  ----  ------  ---------
   0     0       0          0
   1     1       1          1
   2     2       2          2
   3     3      10         10
   4    10      11        101
   5    11      12        102
   6     6      20         20
   7    19      21        201
   8    20      22        202
   9     9     100        100
  10    28     101       1001
  11    29     102       1002
  12    30     110       1010

Cf. A007089 (ter(n)), A048678, A328727, A362090.

a(n) = { if (n==0, 0, n%3, 9*a(n\3) + n%3, 3*a(n/3)); }

from gmpy2 import digits
def A362089(n): return int(digits(n,3).replace('1','01').replace('2','02'),3)
# Chai Wah Wu, Apr 12 2023

A350776 Nonnegative integers whose balanced ternary expansion has no two consecutive nonzero digits.

Original entry on oeis.org

0, 1, 3, 8, 9, 10, 24, 26, 27, 28, 30, 71, 72, 73, 78, 80, 81, 82, 84, 89, 90, 91, 213, 215, 216, 217, 219, 233, 234, 235, 240, 242, 243, 244, 246, 251, 252, 253, 267, 269, 270, 271, 273, 638, 639, 640, 645, 647, 648, 649, 651, 656, 657, 658, 699, 701, 702

Offset: 1

Rémy Sigrist, Jan 15 2022

This sequence is to balanced ternary what A328727 is to ternary.

			The first terms, in decimal and in balanced ternary, are:
  n   a(n)  bter(n)
  --  ----  -------
   1     0        0
   2     1        1
   3     3       10
   4     8      10T
   5     9      100
   6    10      101
   7    24     10T0
   8    26     100T
   9    27     1000
  10    28     1001
  11    30     1010
  12    71    10T0T

Cf. A059095, A328727, A350775.

is(n) = { my (p=0, d); while (n, d=[0, 1, -1][1+n%3]; if (p && d, return (0), n=(n-d)/3; p=d)); 1 }

A350775(n) = 0 iff n belongs to the present sequence.

cp's OEIS Frontend

A328728 a(n) = Sum_{k = 0..w and t_k > 0} (-1)^t_k * 2^k, where Sum_{k = 0..w} t_k * 3^k is the ternary representation of A328727(n).

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A362089 The base-3 expansion of a(n) is obtained by inserting a zero before each nonzero digit of the base-3 expansion of n.

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A350776 Nonnegative integers whose balanced ternary expansion has no two consecutive nonzero digits.

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