A328727 Nonnegative numbers whose base-3 expansion has no two consecutive nonzero digits.

0, 1, 2, 3, 6, 9, 10, 11, 18, 19, 20, 27, 28, 29, 30, 33, 54, 55, 56, 57, 60, 81, 82, 83, 84, 87, 90, 91, 92, 99, 100, 101, 162, 163, 164, 165, 168, 171, 172, 173, 180, 181, 182, 243, 244, 245, 246, 249, 252, 253, 254, 261, 262, 263, 270, 271, 272, 273, 276

Offset

1,3

Comments

This sequence is a ternary variant of A003714, the fibbinary numbers.

Apparently, A122983 gives the distinct values of the first differences of this sequence.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10923 (Terms < 3^13)

Example

The first terms, alongside their ternary representation, are:
  n   a(n)  ter(a(n))
  --  ----  ---------
   1     0          0
   2     1          1
   3     2          2
   4     3         10
   5     6         20
   6     9        100
   7    10        101
   8    11        102
   9    18        200
  10    19        201
  11    20        202
  12    27       1000

Prog

(PARI) is(n, base=3) = my (d=digits(n, base)); for (i=1, #d-1, if (d[i] && d[i+1], return (0))); return (1)
(Python)
from itertools import count, islice
from gmpy2 import digits
def A328727_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 n
A328727_list = list(islice(A328727_gen(), 30)) # Chai Wah Wu, Jan 24 2022

Crossrefs

Cf. A003714, A122983.

Sequence in context: A007086 A047404 A133555 * A032938 A188323 A090892

Adjacent sequences: A328724 A328725 A328726 * A328728 A328729 A328730

Keyword

nonn,base,easy

Author

Rémy Sigrist, Oct 26 2019

Status

approved