A229610 Array: each row starts with the least prime not in a previous row, and each prime p in a row is followed by the least prime > 3*p.

2, 7, 3, 23, 11, 5, 71, 37, 17, 13, 223, 113, 53, 41, 19, 673, 347, 163, 127, 59, 29, 2027, 1049, 491, 383, 179, 89, 31, 6089, 3163, 1481, 1151, 541, 269, 97, 43, 18269, 9491, 4447, 3457, 1627, 809, 293, 131, 47, 54829, 28477, 13367, 10391, 4889, 2437, 881

Offset: 1

Author

Clark Kimberling, Sep 26 2013

Keywords

• nonn
• tabl

Comments

Conjectures: (row 1) = A076656, (column 1) = A164958, and for each row r(k), the limit of r(k)/3^k exists. For rows 1 to 4, the respective limits are 0.928655..., 1.447047..., 2.038260..., 4.753271... .

Examples

			Northwest corner:
   2,  7,  23,  71,  223,  673, ...
   3, 11,  37, 113,  347, 1049, ...
   5, 17,  53, 163,  491, 1481, ...
  13, 41, 127, 383, 1151, 3457, ...
  19, 59, 179, 541, 1627, 4889, ...
  29, 89, 269, 809, 2437, 7331, ...
		

Crossrefs

Cf. A076656, A164958, A229607, A229608, A229609.

Programs

Mathematica

seqL = 14; arr2[1] = {2}; Do[AppendTo[arr2[1], NextPrime[3*Last[arr2[1]]]], {seqL}]; Do[tmp = Union[Flatten[Map[arr2, Range[z]]]]; arr2[z] = {Prime[NestWhile[# + 1 &, 1, PrimePi[tmp[[#]]] - # == 0 &]]}; Do[AppendTo[arr2[z], NextPrime[3*Last[arr2[z]]]], {seqL}], {z, 2, 12}]; m = Map[arr2, Range[12]]; m // TableForm
t = Table[m[[n - k + 1]][[k]], {n, 12}, {k, n, 1, -1}] // Flatten (* Peter J. C. Moses, Sep 26 2013 *)

Extensions

Incorrect comment deleted by Peter Munn, Aug 15 2017