A359300 -id:A359300 - cp's OEIS frontend

A359298 Array T(n, k) read by antidiagonals: for n >= 0 and k >= 0, row n lists the positive integers m such that m - k is prime or 1, and m - h, for 0 <= h < k, is not prime.

1, 2, 4, 3, 6, 9, 5, 8, 15, 10, 7, 12, 21, 16, 27, 11, 14, 25, 22, 35, 28, 13, 18, 33, 26, 51, 36, 95, 17, 20, 39, 34, 57, 52, 119, 96, 19, 24, 45, 40, 65, 58, 145, 120, 121, 23, 30, 49, 46, 77, 66, 187, 146, 147, 122, 29, 32, 55, 50, 87, 78, 205, 188, 189

Offset: 1

Clark Kimberling, Jan 01 2023

Essentially, for n >= 0, row n lists the numbers whose distance down to the nearest prime is n.

			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.

Cf. A000040, A008578, A359299, A359300.

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 *)

A359299 Array T(n, k) read by antidiagonals: for n >= 0 and k >= 0, row n lists the positive integers m such that m + k is prime or 1, and m + h, for 0 <= h < k, is not prime.

Original entry on oeis.org

1, 2, 4, 3, 6, 9, 5, 10, 15, 8, 7, 12, 21, 14, 25, 11, 16, 27, 20, 33, 24, 13, 18, 35, 26, 49, 32, 91, 17, 22, 39, 34, 55, 48, 121, 90, 19, 28, 45, 38, 63, 54, 143, 120, 119, 23, 30, 51, 44, 75, 62, 185, 142, 141, 118, 29, 36, 57, 50, 85, 74, 205, 184, 183

Offset: 1

Clark Kimberling, Jan 01 2023

Essentially, for n >= 0, row n lists the numbers whose distance down to the nearest prime is n.

			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.

Cf. A000040, A008578, A359298, A359300.

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 *)

cp's OEIS Frontend

A359298 Array T(n, k) read by antidiagonals: for n >= 0 and k >= 0, row n lists the positive integers m such that m - k is prime or 1, and m - h, for 0 <= h < k, is not prime.

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