OFFSET
0,5
COMMENTS
All numbers appear in this sequence. Numbers of the form (3^n-1)/2 (A003462(n)) have n 1's in their ternary expression.
The longest run of zeros possible in this sequence is 2, as the last digit of the ternary expression of the integers cycles between 0, 1, and 2, meaning that at least one of three consecutive numbers has a 1 in its ternary expression.
LINKS
Wikipedia, Ternary numeral system.
EXAMPLE
For n = 43, the ternary expression of 43 is 1121. The length of the runs of 1's in the ternary expression of 43 are 2 and 1, respectively. The larger of these two values is 2, so a(43) = 2.
n [ternary n] a(n)
0 [ 0] 0
1 [ 1] 1
2 [ 2] 0
3 [ 1 0] 1
4 [ 1 1] 2
5 [ 1 2] 1
6 [ 2 0] 0
7 [ 2 1] 1
8 [ 2 2] 0
9 [ 1 0 0] 1
10 [ 1 0 1] 1
11 [ 1 0 2] 1
12 [ 1 1 0] 2
13 [ 1 1 1] 3
14 [ 1 1 2] 2
15 [ 1 2 0] 1
16 [ 1 2 1] 1
17 [ 1 2 2] 1
18 [ 2 0 0] 0
19 [ 2 0 1] 1
20 [ 2 0 2] 0
MATHEMATICA
Table[Max@FoldList[If[#2==1, #1+1, 0]&, 0, IntegerDigits[n, 3]], {n, 0, 90}]
Table[Max[Length/@Select[Split[IntegerDigits[n, 3]], MemberQ[#, 1]&]], {n, 0, 100}]/.(-\[Infinity]->0) (* Harvey P. Dale, Jan 07 2023 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Joshua Oliver, Dec 04 2019
STATUS
approved