A192177 Array determined by distance down to nearest prime.

1, 2, 5, 3, 7, 10, 4, 9, 16, 11, 6, 13, 22, 17, 28, 8, 15, 26, 23, 36, 29, 12, 19, 34, 27, 52, 37, 96, 14, 21, 40, 35, 58, 53, 120, 97, 18, 25, 46, 41, 66, 59, 146, 121, 122, 20, 31, 50, 47, 78, 67, 188, 147, 148, 123, 24, 33, 56, 51, 88, 79, 206, 189, 190, 149, 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 is a prime.

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

Every positive integer occurs exactly once, so that as a sequence, A192177 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
5....7....9....13...15...19
10...16...22...26...34...40
11...17...23...27...35...41
28...36...52...58...66...78
...
For example, 16 is in row 3 because 16 - 3 is prime, unlike 16 - 1 and 16 - 2.
		

Crossrefs

Cf. A192175, A192176, A192178, A192179.

Programs

Mathematica

z = 5000; (* z = number of primes used *)
row[1] = (#1[[1]] &) /@ Cases[Array[{#1, PrimeQ[#1 - 1] || #1 == 1 || #1 == 2} &, {z}], {_, True}];
Do[row[x] = Complement[(#1[[1]] &) /@  Cases[Array[{#1, PrimeQ[#1 - x]} &, {z}], {_, True}], Flatten[Array[row, {x - 1}]]], {x, 2, 10}];
TableForm[Array[row, {10}]]  (* A192177 array *)
Flatten[Table[row[k][[n - k + 1]], {n, 1, 11}, {k, 1,
   n}]]  (* A192177 sequence *)
(* by Peter J. C. Moses, Jun 24 2011 *)