A359298 - OEIS

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

(list; table; graph; refs; listen; history; text; internal format)

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 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

Cf. A000040, A008578, A359299, A359300.

Sequence in context: A163280 A056537 A293054 * A255127 A083221 A246278

Adjacent sequences: A359295 A359296 A359297 * A359299 A359300 A359301

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 01 2023

STATUS

approved