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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.
3
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
1,1
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... .
EXAMPLE
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, ...
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 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Sep 26 2013
EXTENSIONS
Incorrect comment deleted by Peter Munn, Aug 15 2017
STATUS
approved