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%I #14 Aug 17 2017 22:36:37
%S 2,7,3,23,11,5,71,37,17,13,223,113,53,41,19,673,347,163,127,59,29,
%T 2027,1049,491,383,179,89,31,6089,3163,1481,1151,541,269,97,43,18269,
%U 9491,4447,3457,1627,809,293,131,47,54829,28477,13367,10391,4889,2437,881
%N 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.
%C 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... .
%e Northwest corner:
%e 2, 7, 23, 71, 223, 673, ...
%e 3, 11, 37, 113, 347, 1049, ...
%e 5, 17, 53, 163, 491, 1481, ...
%e 13, 41, 127, 383, 1151, 3457, ...
%e 19, 59, 179, 541, 1627, 4889, ...
%e 29, 89, 269, 809, 2437, 7331, ...
%t 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 t = Table[m[[n - k + 1]][[k]], {n, 12}, {k, n, 1, -1}] // Flatten (* _Peter J. C. Moses_, Sep 26 2013 *)
%Y Cf. A076656, A164958, A229607, A229608, A229609.
%K nonn,tabl
%O 1,1
%A _Clark Kimberling_, Sep 26 2013
%E Incorrect comment deleted by _Peter Munn_, Aug 15 2017