OFFSET
1,2
COMMENTS
Essentially, for n >= 0, row n lists the numbers whose distance down to the nearest prime is n.
EXAMPLE
Corner:
1 2 3 5 7 11 13 17 19 23 29
4 6 10 12 16 18 22 28 30 36 40
9 15 21 27 35 39 45 51 57 65 69
8 14 20 26 34 38 44 50 56 64 68
25 33 49 55 63 75 85 93 123 133 145
24 32 48 54 62 74 84 92 122 132 144
Row 0 includes 19 because 19 is prime, and 19 - 19 = 0.
Row 1 includes 10 because the nearest prime up from 10 is 11, and 11 - 10 = 1.
MATHEMATICA
rows = 15;
row[0] = Join[{1}, Map[Prime, Range[250]]]; Table[
row[z] = Map[#[[1]] &, Select[Map[{#, Apply[And,
Join[{MemberQ[row[0], # + z]}, Table[! MemberQ[row[0], # + k],
{k, 0, z - 1}]]]} &,
Range[Max[row[z - 1]]]], #[[2]] &]], {z, rows}];
Table[row[z], {z, 0, rows}] // ColumnForm (* A359299 array *)
t[n_, k_] := row[n - 1][[k]]
u = Table[t[n - k + 1, k], {n, 15}, {k, n, 1, -1}] //
Flatten (* A359299 sequence *)
(* Peter J. C. Moses Dec 18 2022 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Jan 01 2023
STATUS
approved