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A229608
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Square array read by antidiagonals downwards: 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 > 2*p.
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5
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2, 5, 3, 11, 7, 13, 23, 17, 29, 19, 47, 37, 59, 41, 31, 97, 79, 127, 83, 67, 43, 197, 163, 257, 167, 137, 89, 53, 397, 331, 521, 337, 277, 179, 107, 61, 797, 673, 1049, 677, 557, 359, 223, 127, 71, 1597, 1361, 2099, 1361, 1117, 719, 449, 257, 149, 73, 3203
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OFFSET
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1,1
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COMMENTS
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Conjectures: (row 1) = A055496, (column 1) = A193507, and for each row r(k), the limit of r(k)/2^k exists. For rows 1 to 4, the respective limits are 1.569985..., 2.677285..., 8.230592..., 10.709142...; see Franklin T. Adams-Watters's comment at A055496.
Column 1 diverges from A193507 at A(14,1) = 113, a prime not in A193507. 113 is in column 1 as it does not follow a prime in a row: 107 follows 53 and 127 follows 59, the next prime after 53. - Peter Munn, Jul 30 2017
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LINKS
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EXAMPLE
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Northwest corner:
2 5 11 23 47 97 197
3 7 17 37 79 163 331
13 29 59 127 257 521 1049
19 41 83 167 337 677 1361
31 67 137 277 557 1117 2237
43 89 179 359 719 1439 2879
53 107 223 449 907 1823 3659
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MATHEMATICA
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seqL = 14; arr2[1] = {2}; Do[AppendTo[arr2[1], NextPrime[2*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[2*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 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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Incorrect comment deleted and example extended by Peter Munn, Jul 30 2017
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STATUS
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approved
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