A349297 Triangle T(n,k) = 1 if both n and k are even or if n and k are divisible by 3.

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

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

Cf. A005843, A008585, A047229, A054521.

Sequence in context: A282317 A212126 A144605 * A349317 A154103 A116178

Adjacent sequences: A349294 A349295 A349296 * A349298 A349299 A349300

Keyword

nonn,easy,tabl

Author

Michael De Vlieger, Nov 13 2021

Status

approved