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.

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

1,2

Comments

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

Links

Table of n, a(n) for n=1..64.

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

Cf. A000040, A008578, A359298, A359300.

Sequence in context: A255127 A083221 A246278 * A363473 A361748 A372337

Adjacent sequences: A359296 A359297 A359298 * A359300 A359301 A359302

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 01 2023

Status

approved