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

1,2

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.

Links

Table of n, a(n) for n=1..66.

Example

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.

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 *)

Crossrefs

Cf. A192175, A192176, A192177, A192179.

Sequence in context: A096878 A249162 A134563 * A201914 A331217 A021398

Adjacent sequences: A192175 A192176 A192177 * A192179 A192180 A192181

Keyword

nonn,tabl

Author

Clark Kimberling, Jun 24 2011

Status

approved