A229609 Array: each row starts with the least prime not in a previous row, and each prime p in a row is followed by the greatest prime < 3*p.

2, 5, 3, 13, 7, 11, 37, 19, 31, 17, 109, 53, 89, 47, 23, 317, 157, 263, 139, 67, 29, 947, 467, 787, 409, 199, 83, 41, 2837, 1399, 2357, 1223, 593, 241, 113, 43, 8501, 4177, 7069, 3659, 1777, 719, 337, 127, 59, 25471, 12527, 21193, 10973, 5323, 2153, 1009

Offset: 1

Author

Clark Kimberling, Sep 26 2013

Keywords

• nonn
• tabl

Comments

Conjectures: (row 1) = A126031, (column 1) = A164952, and for each row r(k), the limit of r(k)/3^k exists. For rows 1 to 4, the respective limits are 0.431270..., 0.636059..., 3.229697..., 5.015914... .

Examples

			Northwest corner:
   2,  5,  13,  37,  109,  317, ...
   3,  7,  19,  53,  157,  467, ...
  11, 31,  89, 263,  787, 2357, ...
  17, 47, 139, 409, 1223, 3659, ...
  23, 67, 199, 593, 1777, 5323, ...
  29, 83, 241, 719, 2153, 6451, ...
		

Crossrefs

Cf. A126031, A164952, A229607, A229608, A229610.

Programs

Mathematica

seqL = 14; arr1[1] = {2}; Do[AppendTo[arr1[1], NextPrime[3*Last[arr1[1]], -1]], {seqL}];  Do[tmp = Union[Flatten[Map[arr1, Range[z]]]]; arr1[z] = {Prime[NestWhile[# + 1 &, 1, PrimePi[tmp[[#]]] - # == 0 &]]}; Do[AppendTo[arr1[z], NextPrime[3*Last[arr1[z]], -1]], {seqL}], {z, 2, 22}]; m = Map[arr1, Range[22]]; 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