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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 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

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