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.

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

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