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%I #18 Aug 17 2017 22:35:55
%S 2,3,11,5,19,17,7,37,31,29,13,73,61,53,41,23,139,113,103,79,47,43,277,
%T 223,199,157,89,59,83,547,443,397,313,173,113,67,163,1093,883,787,619,
%U 337,223,131,71,317,2179,1759,1571,1237,673,443,257,139,97,631
%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 greatest prime < 2*p.
%C Conjectures: (row 1) = A006992, (column 1) = A104272, and for each row r(k), the limit of r(k)/2^k exists. For rows 1 to 4, the respective limits are 0.303976..., 4.249137..., 6.857407..., 12.235210... .
%e Northwest corner:
%e 2, 3, 5, 7, 13, 23, 43, 83, ...
%e 11, 19, 37, 73, 139, 277, 547, 1093, ...
%e 17, 31, 61, 113, 223, 443, 883, 1759, ...
%e 29, 53, 103, 199, 397, 787, 1571, 3137, ...
%e 41, 79, 157, 313, 619, 1237, 2473, 4943, ...
%e 47, 89, 173, 337, 673, 1327, 2647, 5281, ...
%t seqL = 14; arr1[1] = {2}; Do[AppendTo[arr1[1], NextPrime[2*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[2*Last[arr1[z]], -1]], {seqL}], {z, 2, 12}]; m = Map[arr1, 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. A006992, A104272, A229608, A229609, A229610.
%K nonn,tabl
%O 1,1
%A _Clark Kimberling_, Sep 26 2013
%E Incorrect comment deleted by _Peter Munn_, Aug 15 2017
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