

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.


5



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

1,1


COMMENTS

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. AdamsWatters's comment at A055496.
The above conjecture row 1 = A055496 is true; additionally, row 2 = A065545; row 3 = A065546; the first 5 terms of row 6 are a contiguous subsequence of A064934; and column 1 = A194598.  Bob Selcoe, Oct 27 2015; corrected by Peter Munn, Jul 30 2017
The conjecture for column 1 is true iff A194598 and A193507 are equivalent. Is this the case?  Bob Selcoe, Oct 29 2015
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


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
43 89 179 359 719 1439 2879
53 107 223 449 907 1823 3659


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, A193507, 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


EXTENSIONS

Incorrect comment deleted and example extended by Peter Munn, Jul 30 2017


STATUS

approved



