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 8 12 14 18 20 24 30 32 38
9 15 21 25 33 39 45 49 55 63 69
10 16 22 26 34 40 46 50 56 64 70
27 35 51 57 65 77 87 93 117 135 143
28 36 52 58 66 78 88 94 118 136 144
Row 0 includes 19 because 19 is prime, and 19 - 19 = 0.
Row 1 includes 8 because the nearest prime down from 8 is 7, and 8 - 7 = 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 (* A359298 array *)
t[n_, k_] := row[n - 1][[k]];
u = Table[t[n - k + 1, k], {n, 15}, {k, n, 1, -1}] //
Flatten (* A359298 sequence *)
(* Peter J. C. Moses Dec 18 2022 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Jan 01 2023
STATUS
approved