cp's OEIS Frontend

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.

%I A229610 #14 Aug 17 2017 22:36:37
%S A229610 2,7,3,23,11,5,71,37,17,13,223,113,53,41,19,673,347,163,127,59,29,
%T A229610 2027,1049,491,383,179,89,31,6089,3163,1481,1151,541,269,97,43,18269,
%U A229610 9491,4447,3457,1627,809,293,131,47,54829,28477,13367,10391,4889,2437,881
%N 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.
%C A229610 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 A229610 Northwest corner:
%e A229610    2,  7,  23,  71,  223,  673, ...
%e A229610    3, 11,  37, 113,  347, 1049, ...
%e A229610    5, 17,  53, 163,  491, 1481, ...
%e A229610   13, 41, 127, 383, 1151, 3457, ...
%e A229610   19, 59, 179, 541, 1627, 4889, ...
%e A229610   29, 89, 269, 809, 2437, 7331, ...
%t A229610 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 A229610 t = Table[m[[n - k + 1]][[k]], {n, 12}, {k, n, 1, -1}] // Flatten (* _Peter J. C. Moses_, Sep 26 2013 *)
%Y A229610 Cf. A076656, A164958, A229607, A229608, A229609.
%K A229610 nonn,tabl
%O A229610 1,1
%A A229610 _Clark Kimberling_, Sep 26 2013
%E A229610 Incorrect comment deleted by _Peter Munn_, Aug 15 2017