A192179 Array determined by distance to next prime, by antidiagonals.

1, 2, 3, 4, 5, 8, 6, 9, 14, 7, 10, 11, 20, 13, 24, 12, 15, 26, 19, 32, 23, 16, 17, 34, 25, 48, 31, 90, 18, 21, 38, 33, 54, 47, 120, 89, 22, 27, 44, 37, 62, 53, 142, 119, 118, 28, 29, 50, 43, 74, 61, 184, 141, 140, 117, 30, 35, 56, 49, 84, 73, 204, 183, 182, 139, 116

Offset: 1

Author

Clark Kimberling, Jun 24 2011

Keywords

• nonn
• tabl

Comments

Row r : numbers k such that r = (least positive integer h for which k + h is a prime).

Every positive integer occurs exactly once, so that as a sequence, A192179 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....4....6....10....12
3....5....9....11...15....17
8....14...20...26...34....38
7....13...19...25...33....37
24...32...48...54...62....74
...
For example, 14 is in row 3 because 14 + 3 is a prime, unlike 14 + 1 and 14 + 2.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..5050

Crossrefs

Cf. A192175, A192176, A192177, A192178.

Programs

Mathematica

z = 5000;  (* z = number of primes used *)
Do[row[x] = Complement[(#1[[1]] &) /@ Cases[({#1 - x, PrimeQ[#1]} &) /@ (Range[z] + x), {_, True}],
   Flatten[Array[row, {x - 1}]]], {x, 1, 10}]
TableForm[Array[row, {10}]]    (* A192179 array *)
Flatten[Table[row[k][[n - k + 1]], {n, 1, 11}, {k, 1,
   n}]]   (* A192179 sequence *)
(* Peter J. C. Moses, Jun 24 2011 *)