A192178 Array by distance to nearest prime, by antidiagonals.

1, 2, 5, 3, 7, 26, 4, 9, 34, 23, 6, 11, 50, 37, 118, 8, 13, 56, 47, 122, 53, 10, 15, 64, 67, 144, 89, 120, 12, 17, 76, 79, 186, 119, 300, 409, 14, 19, 86, 83, 204, 121, 324, 479, 532, 16, 21, 92, 93, 206, 157, 530, 531, 896, 293, 18, 25, 94, 97, 216, 173, 534, 533, 898, 631, 11

Offset: 1

Author

Clark Kimberling, Jun 24 2011

Keywords

• nonn
• tabl

Comments

Row 1: numbers k such that k = 1 or k = 2 or (k - 1 or k + 1) is a prime.

Row r > 1: numbers k such that k + r or k - r is a prime but k + q and k - q are not, for q = 1, 2, ..., r - 1.

Every positive integer occurs exactly once, so that as a sequence, A192178 is a permutation of the positive integers.

For r > 1, the numbers in row r have the parity of r - 1; e.g., the numbers in row 2 are odd.

Examples

			Northwest corner:
1....2....3....4....6....8....10
5....7....9....11...13...15...17
26...34...50...56...64...76...86
23...37...47...67...79...83...93
118..122..144..186..204..206..216
...
For example, 34 is in row 3 recause its distance to the nearest prime is 3.
		

Crossrefs

Cf. A192175, A192176, A192177, A192179.

Programs

Mathematica

z = 5000; (* z = number of primes used *)
row[1] = (#1[[1]] &) /@ Cases[Array[{#1, PrimeQ[#1 - 1] || PrimeQ[#1 + 1] || #1 == 1 || #1 == 2} &, {z}], {_, True}];
Do[row[x] = Complement[(#1[[1]] &) /@ Cases[Array[{#1, PrimeQ[#1 - x] || PrimeQ[#1 + x]} &, {z}], {_, True}], Flatten[Array[row, {x - 1}]]], {x, 2, 10}];
TableForm[Array[row, {10}]]  (* A192178 array *)
Flatten[Table[row[k][[n - k + 1]], {n, 1, 11}, {k, 1,
   n}]]   (* A192178 sequence *)
(* by Peter J. C. Moses, Jun 24 2011 *)