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 A349298 Positions k in row n of triangles S(n,k) = T(n,k) = 0, where A054521 = S and A349297 = T, or 0 if there are no such k. 1
 0, 0, 0, 0, 5, 0, 7, 0, 0, 5, 11, 0, 13, 7, 5, 10, 0, 17, 0, 19, 5, 15, 7, 14, 11, 23, 0, 5, 10, 15, 20, 25, 13, 0, 7, 21, 29, 5, 25, 31, 0, 11, 22, 17, 5, 7, 10, 14, 15, 20, 21, 25, 28, 30, 35, 0, 37, 19, 13, 26, 5, 15, 25, 35, 41, 7, 35, 43, 11, 33, 5, 10, 20, 25, 35, 40 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Row n is a list of k for which A349297 NOR A054521 is true. Row p > 3 for p prime has the single term p. Nonzero terms in this sequence are of the form k*m > 1, where 3-smooth k > 1 in A003586 and 5-rough m > 1 in A007310, with m mod 6 = +/- 1. LINKS Michael De Vlieger, Table of n, a(n) for n = 1..10635 (rows 1 <= n <= 600, flattened) Michael De Vlieger, 1024-pixel bitmap plotting (n, T(n,k)) in black, otherwise white including for rows containing 0. EXAMPLE Table T(n,k) for 1 <= n <= 16, replacing 0 with "." and 1 with "*", showing terms in row n of this sequence. Rows with no terms are replaced by 0: 1: . 2: . * 3: . . * 4: . * . * 5: . . . . 5 6: . * * * . * 7: . . . . . . 7 8: . * . * . * . * 9: . . * . . * . . * 10: . * . * 5 * . * . * 11: . . . . . . . . . . 11 12: . * * * . * . * * * . * 13: . . . . . . . . . . . . 13 14: . * . * . * 7 * . * . * . * 15: . . * . 5 * . . * 10 . * . . * 16: . * . * . * . * . * . * . * . * --------------------------------------------------- n\k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Hence, row 5 = {5}, row 7 = {7}, row 11 = {11}, row 13 = {13}, row 14 = {7}, row 15 = {5, 10}, and all other rows 1 <= n <= 16 have no terms, thus are assigned 0 by definition. MATHEMATICA With[{nn = 45}, Table[If[Length[#] == 0, {0}, #] &@ Select[Array[# Boole[Xor[Or[Mod[#, 2] == Mod[n, 2] == 0, Mod[#, 3] == Mod[n, 3] == 0], GCD[n, #] != 1]] &, n], # > 0 &], {n, nn}]] // Flatten (* Michael De Vlieger, Dec 08 2021 *) With[{s = Merge[Map[#1 -> #2 & @@ # &, Position[ImageData[#], 0.]], Identity]}, Array[If[KeyExistsQ[s, #], Lookup[s, #], {0}] &, ImageDimensions[#][[-1]]] // Flatten] &@ Import["https://oeis.org/A349298/a349298.png"] (* Generate 1024 rows stored in the bitmap image, Michael De Vlieger, Dec 08 2021 *) CROSSREFS Cf. A003586, A007310, A047229, A054521. Sequence in context: A069206 A291800 A091685 * A062824 A292904 A271228 Adjacent sequences: A349295 A349296 A349297 * A349299 A349300 A349301 KEYWORD nonn,tabf AUTHOR Michael De Vlieger, Nov 13 2021 STATUS approved

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Last modified April 21 10:29 EDT 2024. Contains 371852 sequences. (Running on oeis4.)