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A229608 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. 4
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Every prime occurs exactly once. 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.

The above conjecture row 1 = A055496(k) is true; additionally, row 2 = A065545(k); row 3 = A065546(k); row 6 = A064934(k+4); and column 1 = A194598(n). - Bob Selcoe, Oct 27 2015

The conjecture for column 1 is true iff A194598 and A193507 are equivalent. Is this the case? - Bob Selcoe, Oct 29 2015

LINKS

Table of n, a(n) for n=1..56.

EXAMPLE

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

MATHEMATICA

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 *)

CROSSREFS

Cf. A055496, A192507, A229607, A229609, A229610.

Cf. A065545, A065546, A064934, A194598.

Sequence in context: A221183 A178174 A094744 * A185061 A129198 A122442

Adjacent sequences:  A229605 A229606 A229607 * A229609 A229610 A229611

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Sep 26 2013

STATUS

approved

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Last modified March 29 15:10 EDT 2017. Contains 284273 sequences.