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A349297 Triangle T(n,k) = 1 if both n and k are even or if n and k are divisible by 3. 2
0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1
COMMENTS
Excludes S(n,k) such that gcd(n,k) = 1.
Row n in {1,5} mod 6 consists of k zeros; column k in {1,5} mod 6 is always 0.
Row or column p > 5 where p is prime consists of p zeros.
For n = 0 (mod 6), k in A047229 have T(n,k) = 1.
For k = 0 (mod 6), n in A047229 have T(n,k) = 1.
T(n,k) such that n and k both belong to {2,3,4} mod 6 form a "quincunx" or x-shaped checkerboard pattern evident in the table. In A054521, these have the value 0 along with other terms T(n,k) such that gcd(n,k) > 1.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows 1 <= n <= 150, flattened)
Michael De Vlieger, Bitmap magnified 3X showing T(n,k) = 1 in black and 0 in white.
EXAMPLE
Table T(n,k) for 1 <= n <= 16, replacing 0 with "." to accentuate the pattern:
1: .
2: . 1
3: . . 1
4: . 1 . 1
5: . . . . .
6: . 1 1 1 . 1
7: . . . . . . .
8: . 1 . 1 . 1 . 1
9: . . 1 . . 1 . . 1
10: . 1 . 1 . 1 . 1 . 1
11: . . . . . . . . . . .
12: . 1 1 1 . 1 . 1 1 1 . 1
13: . . . . . . . . . . . . .
14: . 1 . 1 . 1 . 1 . 1 . 1 . 1
15: . . 1 . . 1 . . 1 . . 1 . . 1
16: . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1
---------------------------------------------------
n\k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
MATHEMATICA
Table[Array[Boole@ Or[Mod[#, 2] == Mod[n, 2] == 0, Mod[#, 3] == Mod[n, 3] == 0] &, n], {n, 13}]
CROSSREFS
Sequence in context: A282317 A212126 A144605 * A349317 A154103 A116178
KEYWORD
nonn,easy,tabl
AUTHOR
Michael De Vlieger, Nov 13 2021
STATUS
approved

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Last modified April 14 10:04 EDT 2024. Contains 371657 sequences. (Running on oeis4.)