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A330168
Length of the longest run of 2's in the ternary expression of n.
3
0, 0, 1, 0, 0, 1, 1, 1, 2, 0, 0, 1, 0, 0, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 3, 0, 0, 1, 0, 0, 1, 1, 1, 2, 0, 0, 1, 0, 0, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 4, 0, 0, 1, 0, 0, 1, 1, 1, 2, 0
OFFSET
0,9
COMMENTS
All numbers appear in this sequence. Numbers of the form 3^n-1 (A024023(n)) have n 2'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 2 in its ternary expression.
FORMULA
a(A024023(n)) = a(3^n-1) = n.
a(n) = 0 iff n is in A005836.
EXAMPLE
For n = 74, the ternary expression of 74 is 2202. The length of the runs of 2's in the ternary expression of 74 are 2 and 1, respectively. The larger of these two values is 2, so a(74) = 2.
n [ternary n] a(n)
0 [ 0] 0
1 [ 1] 0
2 [ 2] 1
3 [ 1 0] 0
4 [ 1 1] 0
5 [ 1 2] 1
6 [ 2 0] 1
7 [ 2 1] 1
8 [ 2 2] 2
9 [ 1 0 0] 0
10 [ 1 0 1] 0
11 [ 1 0 2] 1
12 [ 1 1 0] 0
13 [ 1 1 1] 0
14 [ 1 1 2] 1
15 [ 1 2 0] 1
16 [ 1 2 1] 1
17 [ 1 2 2] 2
18 [ 2 0 0] 1
19 [ 2 0 1] 1
20 [ 2 0 2] 1
MATHEMATICA
Table[Max@FoldList[If[#2==2, #1+1, 0]&, 0, IntegerDigits[n, 3]], {n, 0, 90}]
CROSSREFS
Equals zero iff n is in A005836.
Sequence in context: A147645 A091970 A093955 * A081603 A273513 A330005
KEYWORD
nonn,base
AUTHOR
Joshua Oliver, Dec 04 2019
STATUS
approved