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

Author

Rémy Sigrist, Oct 26 2019

Keywords

• nonn
• base
• easy

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.

Examples

			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
		

Links

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

Crossrefs

Cf. A003714, A122983.

Programs

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