This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A349298 #10 Dec 09 2021 01:00:49
%S A349298 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,
%T A349298 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,
%U A349298 35,0,37,19,13,26,5,15,25,35,41,7,35,43,11,33,5,10,20,25,35,40
%N 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.
%C A349298 Row n is a list of k for which A349297 NOR A054521 is true.
%C A349298 Row p > 3 for p prime has the single term p.
%C A349298 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.
%H A349298 Michael De Vlieger, <a href="/A349298/b349298.txt">Table of n, a(n) for n = 1..10635</a> (rows 1 <= n <= 600, flattened)
%H A349298 Michael De Vlieger, <a href="/A349298/a349298.png">1024-pixel bitmap</a> plotting (n, T(n,k)) in black, otherwise white including for rows containing 0.
%e A349298 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:
%e A349298 1: .
%e A349298 2: . *
%e A349298 3: . . *
%e A349298 4: . * . *
%e A349298 5: . . . . 5
%e A349298 6: . * * * . *
%e A349298 7: . . . . . . 7
%e A349298 8: . * . * . * . *
%e A349298 9: . . * . . * . . *
%e A349298 10: . * . * 5 * . * . *
%e A349298 11: . . . . . . . . . . 11
%e A349298 12: . * * * . * . * * * . *
%e A349298 13: . . . . . . . . . . . . 13
%e A349298 14: . * . * . * 7 * . * . * . *
%e A349298 15: . . * . 5 * . . * 10 . * . . *
%e A349298 16: . * . * . * . * . * . * . * . *
%e A349298 ---------------------------------------------------
%e A349298 n\k 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
%e A349298 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.
%t A349298 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 *)
%t A349298 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 *)
%Y A349298 Cf. A003586, A007310, A047229, A054521.
%K A349298 nonn,tabf
%O A349298 1,5
%A A349298 _Michael De Vlieger_, Nov 13 2021